// Numbas version: exam_results_page_options
{"name": "Mensuration", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>Area and Volume Questions</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "None specified"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Q1 Circle mensuration problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/circle-sector-area.gif", "/srv/numbas/media/question-resources/circle-sector-area.gif"], ["question-resources/circle-segment-area.gif", "/srv/numbas/media/question-resources/circle-segment-area.gif"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"circle": {"definition": "\n      var c = document.createElement('canvas');\n        $(c).attr('width',600).attr('height',450);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.beginPath();\n        context.arc(200, 200, 150, 50, Math.PI*2, true); \n        context.closePath();\n        context.fill();\n       \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'Perimeter ='+ p +'m';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = 'r';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-2*Math.PI);\n        context.fillText(hstring,70,-5);\n\n        var hstring = '____________';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(2*Math.PI);\n        context.fillText(hstring,-10,-200);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["p", "number"]]}, "ang": {"definition": "var c = document.createElement('canvas');\n$(c).attr('width',300).attr('height',300);\nvar ctx = c.getContext('2d');\n\nvar angle = Math.PI *((a-(Math.PI/2))/180);  // == 45 degrees\nvar cx = 150;\nvar cy = 150;\nvar radius = 100;\n\nangle-=Math.PI/2;\nctx.lineWidth = 2;\nctx.strokeStyle = 'red';\n\n// draw the red line at the desired angle\nctx.beginPath();\nctx.moveTo(cx, cy);\nctx.arc(cx, cy, radius, angle, angle);\nctx.stroke();\n\n// draw the bulls-eyed circle\nctx.beginPath();\nctx.strokeStyle = 'black';\nctx.arc(cx, cy, radius, 0, Math.PI * 2);\nctx.moveTo(cx - radius, cy);\nctx.lineTo(cx + radius, cy);\nctx.moveTo(cx, cy - radius);\nctx.lineTo(cx, cy + radius);\nctx.stroke();\n\n\n\nreturn c;", "type": "html", "language": "javascript", "parameters": [["a", "number"]]}, "circle1": {"definition": "\n      var c = document.createElement('canvas');\n        $(c).attr('width',600).attr('height',450);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.beginPath();\n        context.arc(200, 200, 150, 50, Math.PI*2, true); \n        context.closePath();\n        context.fill();\n       \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'Area ='+ p +'m^2';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = 'r';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-2*Math.PI);\n        context.fillText(hstring,70,-5);\n\n        var hstring = '____________';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(2*Math.PI);\n        context.fillText(hstring,-10,-200);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["p", "number"]]}}, "ungrouped_variables": ["r", "area1", "ans1", "area12", "per2", "per22", "ans2", "ans3", "ans4", "sect", "rad", "ans5", "rds", "ans6", "sect1", "ans7", "ans8", "area5", "circ6"], "tags": ["area of a circle", "area of a sector", "canvas", "Circle", "circle", "function", "graphic", "Perimeter", "perimeter", "rebelmaths", "Sector", "sector", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>part&nbsp;1</p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>radius(r) = &nbsp;$\\frac{\\text{Perimeter}}{2 \\times pi} = \\var{ans7}m$</p>\n<p></p>\n<p>part&nbsp;2</p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>radius(r)=&nbsp;$\\sqrt\\frac{(\\text{area})}{pi}&nbsp;= \\var{ans8}m$</p>\n<p></p>\n<p>part 3</p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>radius(r)= $\\sqrt\\frac{(\\text{area})}{pi}$</p>\n<p></p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>$2 \\times \\pi \\times r[0] = \\var{ans1}m$</p>\n<p></p>\n<p>Part 4</p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>Therefore;</p>\n<p>radius(r)= $\\frac{(\\text{perimter})}{2 \\times \\pi}$</p>\n<p>$\\frac{\\var{per22}}{2 \\times \\pi} = \\var{r[1]}m$</p>\n<p></p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>$\\pi \\times&nbsp;\\var{r[1]}^2 = \\var{ans2}m^2$</p>\n<p></p>\n<p>Part&nbsp;5</p>\n<p>$\\frac{\\pi \\times \\var{r[2]}}{2} + 2 \\times \\var{r[2]} = \\var{ans3}$</p>\n<p>$\\frac{\\pi \\times \\var{r[2]}^2}{4} = \\var{ans4}$</p>\n<p></p>\n<p>Part&nbsp;6</p>\n<p><img src=\"resources/question-resources/circle-sector-area.gif\" width=\"247\" height=\"148\"/><img src=\"resources/question-resources/circle-segment-area.gif\" width=\"140\" height=\"145\"/></p>\n<p>where theta is in radians.</p>\n<p>$\\frac{\\var{rds}}{2} \\times \\var{rad}^2= \\var{ans5}$</p>\n<p>$\\frac{1}{2} \\times (\\var{rds} - sin(\\var{rds})) \\times \\var{rad}^2= \\var{ans6}$</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>{circle(circ6)}</p>\n<p>The length of the circumference of a circle is $\\var{circ6}m$. Find the length of the radius of the circle.</p>\n<p>[[0]]&nbsp;$m$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans8}", "strictPrecision": false, "minValue": "{ans8}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>{circle1(area5)}</p>\n<p>The area of a&nbsp;circle&nbsp;is&nbsp;$\\var{area5}m^2$. Find&nbsp;the radius&nbsp;of the circle?</p>\n<p>[[0]]m</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans7}", "strictPrecision": false, "minValue": "{ans7}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{circle1(area12)}</p>\n<p>This circle&nbsp;has an area of $\\var{area12}m^2$. Calculate the perimeter of this circle?</p>\n<p>[[0]]m</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First you need to find the radius of this circle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{circle(per22)}</p>\n<p>Calculate the area of a&nbsp;circle which has a&nbsp;perimeter of $\\var{per22}m^2$.</p>\n<p>[[0]]&nbsp;$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First you need to find the radius of this circle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>A steel plate is in the shape of a quadrant of a circle and has a radius of $\\var{r[2]}$m. Calculate&nbsp;the perimeter of this plate and the area of the segment.</p>\n<p>Perimeter =&nbsp;[[0]]m</p>\n<p>Area =&nbsp;[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Remember the formula for the area of a sector uses radian measure for the angle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "strictPrecision": false, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{ang(sect1)}</p>\n<p>A sector of a circle makes an angle of $\\var{sect}$ degrees at the centre and has a radius of $\\var{rad}cm$. Calculate the area of the sector and the area of the segment.</p>\n<p>The angle is the obtuse&nbsp;angle between the positive x-axis&nbsp;line, (3 o'clock point) and the red line, in an anti-clockwise motion.</p>\n<p>Area of sector =&nbsp;[[0]]$cm^2$</p>\n<p>Area of segment =&nbsp;[[1]]$cm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The following diagrams should help to explain the question.</p>\n<p><img src=\"resources/question-resources/circle-sector-area.gif\" width=\"282\" height=\"169\"/><img src=\"resources/question-resources/circle-segment-area.gif\" width=\"237\" height=\"246\"/></p>\n<p>where theta is in radians.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans5}", "strictPrecision": false, "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans6}", "strictPrecision": false, "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following to <strong>two decimal places</strong>.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans8": {"definition": "circ6/(2 * pi)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "rad": {"definition": "random(4..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "rad", "description": ""}, "rds": {"definition": "precround(radians(sect),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "rds", "description": ""}, "sect1": {"definition": "(180-sect)+270", "templateType": "anything", "group": "Ungrouped variables", "name": "sect1", "description": ""}, "per22": {"definition": "precround(per2,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "per22", "description": ""}, "ans1": {"definition": "2*pi*r[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "pi*(r[1]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(pi*r[2])/2 + 2*r[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "(pi*(r[2]^2))/4", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "(rds/2)*rad^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "0.5*(rds-sin(rds))*rad^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans7": {"definition": "sqrt(area5/(pi))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "per2": {"definition": "2*pi*r[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "per2", "description": ""}, "circ6": {"definition": "random(120..160)", "templateType": "anything", "group": "Ungrouped variables", "name": "circ6", "description": ""}, "r": {"definition": "shuffle(3..7#0.1)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "sect": {"definition": "random(95..170)", "templateType": "anything", "group": "Ungrouped variables", "name": "sect", "description": ""}, "area5": {"definition": "random(1500..2000)", "templateType": "anything", "group": "Ungrouped variables", "name": "area5", "description": ""}, "area12": {"definition": "precround(area1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "area12", "description": ""}, "area1": {"definition": "pi*(r[0]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "area1", "description": ""}}, "metadata": {"description": "<p>Circumference and area of a circle</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 Triangle problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula.png", "/srv/numbas/media/question-resources/area-of-a-equilateral-triangle-formula.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"tri": {"definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',200).attr('height',200);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 100\nvar YY = 100\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["h", "number"]]}, "tri1": {"definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',500).attr('height',500);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 200\nvar YY = 200\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["a", "number"]]}}, "ungrouped_variables": ["side1", "ans1", "lent2", "area2", "ans2"], "tags": ["area", "Area", "area of a triangle", "Area of a triangle", "canvas", "function", "graphic", "rebelmaths", "triangle", "Triangle"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part1</p>\n<p><img src=\"resources/question-resources/area-of-a-equilateral-triangle-formula.png\"/></p>\n<p>where a=length of side</p>\n<p>$\\frac{\\sqrt3}{4} \\times \\var{side1}^2= \\var{ans1}m^2$</p>\n<p><strong>Or another method is:</strong></p>\n<p>A = $\\frac{1}{2}$ab $\\sin(c)$ =&nbsp;$\\frac{1}{2}&nbsp;\\times \\var{side1} \\times \\var{side1} \\times&nbsp;\\sin(60) = \\var{ans1}m^2$</p>\n<p></p>\n<p>Formula for perpendicular height&nbsp;of triangle.</p>\n<p>Area&nbsp;= $\\frac{1}{2}&nbsp;\\times $base$&nbsp;&nbsp;\\times$ perpendicular height</p>\n<p>$2 \\times \\frac{\\var{area2}}{\\var{lent2}} = \\var{ans2}m$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the area of an equilateral triangle which has a side of $\\var{side1}$m.</p>\n<p>{tri(side1)}</p>\n<p>[[0]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Calculate the perpendicular height of a&nbsp;triangle whose&nbsp;base length is&nbsp;$\\var{lent2}$m, if the area of this triangle is&nbsp;$\\var{area2}m^2$</p>\n<p>{tri1(lent2)}</p>\n<p>[[0]]$m$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Correct to <strong>2 decimal place</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "(sqrt(3)/4)*side1^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(2*area2)/lent2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "lent2": {"definition": "random(7..12#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent2", "description": ""}, "area2": {"definition": "random(60..70#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "area2", "description": ""}, "side1": {"definition": "random(12..16#0.25)", "templateType": "anything", "group": "Ungrouped variables", "name": "side1", "description": ""}}, "metadata": {"description": "<p>Areas of triangles</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 Rectangle problems", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"rectangle": {"definition": "\n\n      var c = document.createElement('canvas');\n        $(c).attr('width',w+400).attr('height',h+400);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.fillRect(50,50,w*10,h*10);\n        \n        //draw outline\n        context.strokeStyle = '#000';\n        context.lineWidth = 3;\n        context.strokeRect(50,50,w*10,h*10);\n        \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'x'+'m';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = h+'m';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-Math.PI/2);\n        context.fillText(hstring,0,0);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["h", "number"], ["w", "number"]]}}, "ungrouped_variables": ["p", "w", "h", "x", "a", "p1", "w1", "h1", "area1"], "tags": ["Area", "area", "canvas", "function", "graphic", "Perimeter", "perimeter", "rebelmaths", "rectangle", "Rectangle"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1</p>\n<p>Formula for perimeter of rectangle.</p>\n<p>Perimeter = $2 \\times$ width&nbsp;$+ 2 \\times$ length</p>\n<p>Therefore;</p>\n<p>width = $\\frac{(\\text{perimter} -&nbsp;2 \\times length)}{2}$</p>\n<p>$\\frac{(\\var{p} -&nbsp;2 \\times \\var{h})}{2} = \\var{w}m$</p>\n<p>Formula for area&nbsp;of rectangle.</p>\n<p>Area&nbsp;= width $\\times$ length&nbsp;</p>\n<p>$\\var{w} \\times&nbsp;\\var{h} = \\var{a}m^2$</p>\n<p></p>\n<p>Part 2</p>\n<p>Formula for area&nbsp;of rectangle.</p>\n<p>Area&nbsp;= width $\\times$ length&nbsp;</p>\n<p>$\\frac{\\var{area1}}{\\var{h1} } = \\var{w1}$</p>\n<p>Perimeter = $2 \\times$ width&nbsp;$+ 2 \\times$ length</p>\n<p>$2 \\times \\var{w1} + 2 \\times&nbsp;\\var{h1} = \\var{p1}m$</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>{rectangle(h,w)}</p>\n<p>A&nbsp;rectangle has a perimeter of $\\var{p}m$. If the length is $\\var{h}m$, first calculate its width and then its area.&nbsp;</p>\n<p>width =&nbsp;[[0]]m</p>\n<p>area =&nbsp;[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First write the perimeter in terms of x.</p>\n<p>Solve for x.</p>\n<p>Then calculate the area.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{w}", "strictPrecision": false, "minValue": "{w}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "strictPrecision": false, "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{rectangle(h1,w1)}</p>\n<p>Calculate the&nbsp;perimeter of a&nbsp;rectangle which has a length of&nbsp;$\\var{h1}m$, if the&nbsp;area of this rectangle is $\\var{area1}m^2$. First calculate its width.</p>\n<p>width =&nbsp;[[0]]m</p>\n<p>perimeter =&nbsp;[[1]]$m$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First write the areain terms of x.</p>\n<p>Next, find the length of side x.</p>\n<p>Then find the perimeter.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{w1}", "strictPrecision": false, "minValue": "{w1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{p1}", "strictPrecision": false, "minValue": "{p1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Correct to <strong>2 decimal places</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "h*w", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "p1": {"definition": "2*h1+2*w1", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "w": {"definition": "random(5..h-6#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "h": {"definition": "random(15..34)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "h1": {"definition": "random(20..26 except h)", "templateType": "anything", "group": "Ungrouped variables", "name": "h1", "description": ""}, "p": {"definition": "2*h+2*w", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "w1": {"definition": "random(5..h-6#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "w1", "description": ""}, "x": {"definition": "\"x\"", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "area1": {"definition": "h1*w1", "templateType": "anything", "group": "Ungrouped variables", "name": "area1", "description": ""}}, "metadata": {"description": "<p>Area and Perimeter of Rectangles</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q4 Calculating volume of different containers", "extensions": [], "custom_part_types": [], "resources": [["question-resources/1.png", "/srv/numbas/media/question-resources/1.png"], ["question-resources/charles1.1.gif", "/srv/numbas/media/question-resources/charles1.1.gif"], ["question-resources/formula-explanation-sphere-1.jpg", "/srv/numbas/media/question-resources/formula-explanation-sphere-1.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["size1", "size2", "ans1", "ans2", "ans3"], "tags": ["Cone", "cone", "cylinder", "Cylinder", "rebelmaths", "sphere", "Sphere", "volume", "Volume"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part1</p>\n<p>Volume of cylindrical container</p>\n<p>V = $\\pi r^2h$</p>\n<p>$\\pi \\times (\\frac{\\var{size1[0]}}{2})^2 \\times \\var{size2[0]} = \\var{ans1}$</p>\n<p>Part2</p>\n<p>Volume of conical&nbsp;container</p>\n<p>V = $\\frac{1}{3}\\pi r^2h$</p>\n<p>$\\frac{1}{3} \\times\\pi \\times (\\frac{\\var{size1[1]}}{2})^2 \\times \\var{size2[1]} = \\var{ans2}$</p>\n<p>Part3</p>\n<p>Volume of spherical&nbsp;container</p>\n<p>V = $\\frac{4}{3}\\pi r^3$</p>\n<p>$\\frac{4}{3} \\times\\pi \\times (\\frac{\\var{size1[2]}}{2})^3 = \\var{ans3}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p><img src=\"resources/question-resources/1.png\" width=\"116\" height=\"232\"/></p>\n<p>Find the volume of a cylindrical container of height $\\var{size2[0]}cm$ and diameter $\\var{size1[0]}cm$.</p>\n<p>[[0]]&nbsp;$cm^3$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Don't forget to use the radius rather than the diameter.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/charles1.1.gif\" width=\"177\" height=\"186\"/></p>\n<p>Calculate the volume of a conical container of perpendicular height $\\var{size2[1]}cm$ and diameter&nbsp;$\\var{size1[1]}cm$.</p>\n<p>[[0]]&nbsp;$cm^3$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/formula-explanation-sphere-1.jpg\" width=\"186\" height=\"186\"/></p>\n<p>Find the volume of a spherical container of diameter $\\var{size1[2]}cm$.</p>\n<p>[[0]] $cm^3$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following volume questions to 2 decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "pi*(((size1[0])/2)^2)*size2[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(1/3)*(pi*(((size1[1])/2)^2)*size2[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(4/3)*(pi*(((size1[2])/2)^3))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "size1": {"definition": "shuffle(70..100#10)[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "size1", "description": ""}, "size2": {"definition": "shuffle(110..170#10)[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "size2", "description": ""}}, "metadata": {"description": "<p>Calculating the volumes of different containers</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q6 Volume problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/formula-explanation-sphere-1_iSReoSM.jpg", "/srv/numbas/media/question-resources/formula-explanation-sphere-1_iSReoSM.jpg"], ["question-resources/1_Duq4W7D.png", "/srv/numbas/media/question-resources/1_Duq4W7D.png"], ["question-resources/charles1.1_CeMacDN.gif", "/srv/numbas/media/question-resources/charles1.1_CeMacDN.gif"], ["question-resources/hemisphere_31.png", "/srv/numbas/media/question-resources/hemisphere_31.png"], ["question-resources/5.Concrete_Pier_complete_800.jpg", "/srv/numbas/media/question-resources/5.Concrete_Pier_complete_800.jpg"], ["question-resources/cylinder-area.png", "/srv/numbas/media/question-resources/cylinder-area.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["size1", "size2", "ans1", "ans2", "ans3", "vol", "size3", "size4", "ans2a"], "tags": ["cylinder", "Cylinder", "Hemisphere", "hemisphere", "rebelmaths", "volume", "Volume"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part1</p>\n<p>Volume of hemispherical&nbsp;container</p>\n<p>V = $\\frac{4}{3}\\pi r^3$</p>\n<p>$\\frac{4}{3} \\times\\pi \\times (\\frac{\\var{size2[0]}}{2})^3 = \\var{ans1}$</p>\n<p>Part2</p>\n<p>Volume of cylindrical container</p>\n<p>V = $\\pi r^2h$</p>\n<p>$r = \\sqrt \\frac{V}{\\pi h}$</p>\n<p>$Diameter = 2 \\times r$</p>\n<p>$2 \\times \\sqrt \\frac{\\var{vol}}{\\pi \\times \\var{size1}} = \\var{ans2a}$</p>\n<p>Part3</p>\n<p>Volume of cylindrical container</p>\n<p>V = $\\pi r^2h$</p>\n<p>$\\pi \\times (\\frac{\\var{size3}}{2})^2 \\times \\var{size4} = \\var{ans3}$</p>", "rulesets": {}, "parts": [{"prompt": "<p><img src=\"resources/question-resources/hemisphere_31.png\"/></p>\n<p>Calculate the volume of a hemishperical container of&nbsp;diameter $\\var{size2[0]}cm$.</p>\n<p>[[0]]&nbsp;$cm^3$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/cylinder-area.png\"/></p>\n<p>A cylinrical tank has a volume of&nbsp;$\\var{vol}m^3$. If the height of the tank is&nbsp;$\\var{size1}m$, find its diameter length.</p>\n<p>[[0]]&nbsp;$m$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2a}", "strictPrecision": false, "minValue": "{ans2a}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/5.Concrete_Pier_complete_800.jpg\" width=\"148\" height=\"222\"/></p>\n<p>Calculate&nbsp;the volume of concrete required to make a solid cylindrical pillar which has a&nbsp;diameter of $\\var{size3}$ metres and a perpendicular height of&nbsp;$\\var{size4}m$.</p>\n<p>[[0]] $m^3$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following volume questions to 2 decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"size4": {"definition": "random(2..6 #0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "size4", "description": ""}, "size1": {"definition": "random(3.25..6.25 #05)", "templateType": "anything", "group": "Ungrouped variables", "name": "size1", "description": ""}, "size2": {"definition": "shuffle(110..170#10)[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "size2", "description": ""}, "size3": {"definition": "random(0.61..0.89#0.01  except 0.7 except 0.8)", "templateType": "anything", "group": "Ungrouped variables", "name": "size3", "description": ""}, "vol": {"definition": "precround((pi*((ans2)^2)*size1),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "vol", "description": ""}, "ans1": {"definition": "(2/3)*(pi*(((size2[0])/2)^3))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "random(2.5..7#0.25)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(pi*((size3/2)^2)*size4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans2a": {"definition": "ans2*2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2a", "description": ""}}, "metadata": {"description": "<p>Volume Problems</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q5 Oil tanks problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/recttank.png", "/srv/numbas/media/question-resources/recttank.png"], ["question-resources/verttank.png", "/srv/numbas/media/question-resources/verttank.png"], ["question-resources/watrtank.png", "/srv/numbas/media/question-resources/watrtank.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["size", "dia", "per", "price", "vol1", "dia1", "ans1", "vol2", "ans2", "vol3", "ans3"], "tags": ["cubic metres", "litres", "REBEL", "rebel", "Rebel", "rebelmaths", "teame", "Volume", "volume"], "preamble": {"css": "", "js": ""}, "advice": "<p>N.B</p>\n<p>$1m = 1000mm$</p>\n<p>$1m^3 = 1000$litres</p>\n<p>Part 1</p>\n<p>Volume of cylindrical&nbsp;oil tank</p>\n<p>V = $\\pi r^2h$</p>\n<p>V =&nbsp;$\\pi \\times(\\frac{\\var{dia1}}{2\\times1000})^2 \\times \\var{size[0]} = \\var{vol1}$</p>\n<p>Ans = $\\var{vol1} \\times 1000 \\times (\\frac{\\var{price[0]}}{100}) \\times (\\frac{\\var{per[0]}}{100}) = \\var{ans1}$</p>\n<p>Part 2</p>\n<p>Volume of cylindrical&nbsp;oil tank</p>\n<p>V = $\\pi r^2h$</p>\n<p>V =&nbsp;$\\pi \\times(\\frac{\\var{dia[0]}}{2})^2 \\times \\var{size[1]} = \\var{vol2}$</p>\n<p>Ans = $\\var{vol2} \\times 1000 \\times (\\frac{\\var{price[1]}}{100}) &nbsp;= \\var{ans2}$</p>\n<p>Part 3</p>\n<p>V = length $\\times$ breadth&nbsp;$\\times$ height</p>\n<p>V =&nbsp;$\\var{size[2]} \\times \\var{size[3]} \\times \\var{dia[1]} = \\var{vol3}$</p>\n<p>Ans = $\\var{vol3} \\times 1000 \\times (\\frac{\\var{price[2]}}{100}) &nbsp;= \\var{ans3}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p><img src=\"resources/question-resources/recttank.png\"/></p>\n<p>A rectangular oil tank has dimensions&nbsp;$\\var{size[2]}m$ by&nbsp;$\\var{size[3]}m$ by&nbsp;$\\var{dia[1]}m$. Find the cost to fill this tank if the fuel is priced at&nbsp;$\\var{price[2]}$ cent per litre.</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><a href=\"https://www.youtube.com/watch?v=dLhXBuoEUqQ\">Converting metres cubed to Litres</a></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": true, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "0", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p><img src=\"resources/question-resources/verttank.png\" width=\"134\" height=\"163\"/></p>\n<p>Find the cost of a fill of heating oil for a cylindrical oil tank, filled to capacity, $\\var{size[1]}m$ long and&nbsp;$\\var{dia[0]}m$ in diameter. The fuel is priced at $\\var{price[1]}$ cent per litre.</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Be careful to use an accurate value for pi from your calculator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": true, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/watrtank.png\" width=\"229\" height=\"207\"/></p>\n<p>A cylindrical oil tank measures $\\var{size[0]}m$ long and $\\var{dia1}mm$ in diameter. Calculate the cost to fill $\\var{per[0]}$% of the tank, if the fuel is priced at $\\var{price[0]}$ cent per litre.</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": true, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following oil tank questions to the <strong>nearest euro</strong>.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "vol1*1000*(price[0]/100)*(per[0]/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "price": {"definition": "shuffle(76..92#0.1)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "ans3": {"definition": "vol3*1000*price[2]/100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "dia": {"definition": "shuffle(1.2..1.8#0.01)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "dia", "description": ""}, "per": {"definition": "shuffle(60..90#10)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "per", "description": ""}, "vol1": {"definition": "pi*((dia1/2000)^2)*size[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "vol1", "description": ""}, "vol3": {"definition": "size[2]*size[3]*dia[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "vol3", "description": ""}, "vol2": {"definition": "pi*((dia[0]/2)^2)*size[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "vol2", "description": ""}, "dia1": {"definition": "random(810..940#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "dia1", "description": ""}, "ans2": {"definition": "vol2*1000*(price[1]/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "size": {"definition": "shuffle(2.6..3.75#0.01)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "size", "description": ""}}, "metadata": {"description": "<p>Volume of Oil tanks. Converting cubic metres to L.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q7 Track shape problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula_RlGhwyD.png", "/srv/numbas/media/question-resources/area-of-a-equilateral-triangle-formula_RlGhwyD.png"], ["question-resources/115650640143b203406ae67.jpg", "/srv/numbas/media/question-resources/115650640143b203406ae67.jpg"], ["question-resources/display-illustration.jpg", "/srv/numbas/media/question-resources/display-illustration.jpg"], ["question-resources/pfig1.jpg", "/srv/numbas/media/question-resources/pfig1.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["size", "size2", "size3", "ans11", "ans12", "ans21", "ans22", "ans31", "ans32"], "tags": ["area", "Area", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1</p>\n<p>$(2 \\times \\pi \\times \\frac{\\var{size[0]}}{2}) + (2 \\times \\var{size[0]}) = \\var{ans11}m$</p>\n<p>$(\\pi \\times (\\frac{\\var{size[0]}}{2})^2) + (\\var{size[0]}^2) = \\var{ans12}m^2$</p>\n<p></p>\n<p>Part 2</p>\n<p><img src=\"resources/question-resources/area-of-a-equilateral-triangle-formula_RlGhwyD.png\"/></p>\n<p>$(\\pi \\times \\frac{\\var{size[1]}}{2}) + (2 \\times \\var{size[1]}) + (2 \\times \\var{size[1]})&nbsp;= \\var{ans21}m$</p>\n<p>$\\frac{(\\pi \\times (\\frac{\\var{size[1]}}{2})^2)}{2} + (\\var{size[1]}^2) +(\\frac{\\sqrt(3)}{4} \\times (\\var{size[1]}^2)) = \\var{ans22}m^2$</p>\n<p></p>\n<p>Part 3</p>\n<p>$(2 \\times \\pi \\times \\frac{\\var{size3}}{2}) + (2 \\times \\var{size2}) = \\var{ans31}m$</p>\n<p>$(\\pi \\times (\\frac{\\var{size3}}{2})^2) + (\\var{size2} \\times \\var{size3}) = \\var{ans32}m^2$</p>", "rulesets": {}, "parts": [{"prompt": "<p><img src=\"resources/question-resources/115650640143b203406ae67.jpg\"/></p>\n<p>The figure above shows a running track which is made up of a square of side $\\var{size[0]}$ metres and a semi-circle on each end.</p>\n<p>(i) Calculate the perimeter of the running track.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area enclosed by the running track.</p>\n<p>[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "strictPrecision": false, "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "strictPrecision": false, "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/display-illustration.jpg\" width=\"345\" height=\"190\"/></p>\n<p>The figure above is made up of a square of side $\\var{size[1]}$ metres and a semi-circle on one&nbsp;end and an equilateral triangle on the other end.</p>\n<p>(i) Calculate the perimeter of the figure.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area&nbsp;of the figure.</p>\n<p>[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "strictPrecision": false, "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "strictPrecision": false, "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><img src=\"resources/question-resources/pfig1.jpg\"/></p>\n<p>The figure above shows a running track which is made up of a rectangle&nbsp;of length&nbsp;$\\var{size2}$ metres and width $\\var{size3}$ metres &nbsp;and a semi-circle on each end.</p>\n<p>(i) Calculate the perimeter of the running track.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area enclosed by the running track.</p>\n<p>[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "strictPrecision": false, "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "strictPrecision": false, "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following questions to 2 decimal places!!</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"size2": {"definition": "random(45..70)", "templateType": "anything", "group": "Ungrouped variables", "name": "size2", "description": ""}, "size3": {"definition": "random(25..40)", "templateType": "anything", "group": "Ungrouped variables", "name": "size3", "description": ""}, "ans12": {"definition": "(pi*(size[0]/2)^2)+(size[0]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "(2*pi*(size[0]/2))+(2*size[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "(2*pi*(size3/2))+(2*size2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(pi*(size3/2)^2)+(size2*size3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans22": {"definition": "((pi*(size[1]/2)^2)/2)+(size[1]^2)+((sqrt(3)/4)*size[1]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(pi*(size[1]/2))+(2*size[1])+(2*size[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "size": {"definition": "shuffle(25..77#0.2)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "size", "description": ""}}, "metadata": {"description": "<p>Area and perimeter of compound shapes</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/circle-sector-area.gif", "/srv/numbas/media/question-resources/circle-sector-area.gif"], ["question-resources/circle-segment-area.gif", 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