// Numbas version: finer_feedback_settings
{"name": "Simon's copy of 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simon's copy of Q5 Oil tanks problems", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "metadata": {"description": "<p>Volume of Oil tanks. Converting cubic metres to L.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"vol1": {"templateType": "anything", "definition": "pi*((dia1/2000)^2)*size[0]", "name": "vol1", "description": "", "group": "Ungrouped variables"}, "size": {"templateType": "anything", "definition": "shuffle(2.6..3.75#0.01)[0..4]", "name": "size", "description": "", "group": "Ungrouped variables"}, "vol2": {"templateType": "anything", "definition": "pi*((dia[0]/2)^2)*size[1]", "name": "vol2", "description": "", "group": "Ungrouped variables"}, "dia": {"templateType": "anything", "definition": "shuffle(1.2..1.8#0.01)[0..2]", "name": "dia", "description": "", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "definition": "vol1*1000*(price[0]/100)*(per[0]/100)", "name": "ans1", "description": "", "group": "Ungrouped variables"}, "per": {"templateType": "anything", "definition": "shuffle(60..90#10)[0..2]", "name": "per", "description": "", "group": "Ungrouped variables"}, "ans2": {"templateType": "anything", "definition": "vol2*1000*(price[1]/100)", "name": "ans2", "description": "", "group": "Ungrouped variables"}, "dia1": {"templateType": "anything", "definition": "random(810..940#10)", "name": "dia1", "description": "", "group": "Ungrouped variables"}, "price": {"templateType": "anything", "definition": "shuffle(76..92#0.1)[0..3]", "name": "price", "description": "", "group": "Ungrouped variables"}, "vol3": {"templateType": "anything", "definition": "size[2]*size[3]*dia[1]", "name": "vol3", "description": "", "group": "Ungrouped variables"}, "ans3": {"templateType": "anything", "definition": "vol3*1000*price[2]/100", "name": "ans3", "description": "", "group": "Ungrouped variables"}}, "tags": [], "functions": {}, "ungrouped_variables": ["size", "dia", "per", "price", "vol1", "dia1", "ans1", "vol2", "ans2", "vol3", "ans3"], "statement": "<p>Solve the following oil tank questions to the <strong>nearest pound</strong>.</p>", "extensions": [], "preamble": {"js": "", "css": ""}, "rulesets": {}, "advice": "<p>N.B</p>\n<p>1 m = 1000 mm</p>\n<p>1 m$^3$ = 1000 litres</p>\n<p><strong>(a)</strong></p>\n<p>V = length $\\times$ breadth&nbsp;$\\times$ height</p>\n<p>V =&nbsp;$\\var{size[2]} \\times \\var{size[3]} \\times \\var{dia[1]} = \\var{precround(vol3,3)}$m$^3$ (which we convert to litres by $\\times 1000$)</p>\n<p>Ans = $\\var{precround(vol3,3)} \\times 1000 \\times (\\frac{\\var{price[2]}}{100}) &nbsp;= &pound;\\var{precround(ans3,0)}$</p>\n<p><strong></strong></p>\n<p><strong>(b)</strong></p>\n<p>Volume of cylindrical&nbsp;oil tank</p>\n<p>V = $\\pi r^2h$</p>\n<p>V =&nbsp;$\\pi \\times(\\frac{\\var{dia[0]}}{2})^2 \\times \\var{size[1]} = \\var{precround(vol2,3)}$m$^3$ (which we convert to litres by $\\times 1000$)</p>\n<p>Ans = $\\var{precround(vol2,3)} \\times 1000 \\times (\\frac{\\var{price[1]}}{100}) &nbsp;= &pound;\\var{precround(ans2,0)}$</p>\n<p><strong>(c)</strong></p>\n<p>Volume of cylindrical&nbsp;oil tank</p>\n<p>V = $\\pi r^2h$</p>\n<p>Remember to convert from mm to m by dividing the diameter by 1000:</p>\n<p>V =&nbsp;$\\pi \\times(\\frac{\\var{dia1}}{2\\times1000})^2 \\times \\var{size[0]} = \\var{precround(vol1,3)}$m$^3$ (which we convert to litres by $\\times 1000$)</p>\n<p>Ans = $\\var{precround(vol1,3)} \\times 1000 \\times (\\frac{\\var{price[0]}}{100}) \\times (\\frac{\\var{per[0]}}{100}) = &pound;\\var{precround(ans1,0)}$</p>\n<p></p>", "parts": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "sortAnswers": false, "steps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "type": "information", "prompt": "<p>Note 1000 litres = 1m$^3$</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}}], "gaps": [{"variableReplacementStrategy": "originalfirst", "strictPrecision": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "allowFractions": false, "minValue": "{ans3}", "mustBeReducedPC": 0, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "showFeedbackIcon": true, "precision": "0", "correctAnswerStyle": "plain", "marks": 1, "type": "numberentry", "showPrecisionHint": false, "scripts": {}, "maxValue": "{ans3}"}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "stepsPenalty": 0, "variableReplacements": [], "marks": 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;$\\var{price[2]}$ pence per litre.</p>\n<p>&pound;[[0]]</p>", "type": "gapfill", "unitTests": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "strictPrecision": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "allowFractions": false, "minValue": "{ans2}", "mustBeReducedPC": 0, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "showFeedbackIcon": true, "precision": 0, "correctAnswerStyle": "plain", "marks": 1, "type": "numberentry", "showPrecisionHint": false, "scripts": {}, "maxValue": "{ans2}"}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacements": [], "marks": 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 $\\var{price[1]}$ pence per litre.</p>\n<p>&pound;[[0]]</p>", "type": "gapfill", "unitTests": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "strictPrecision": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "allowFractions": false, "minValue": "{ans1}", "mustBeReducedPC": 0, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "showFeedbackIcon": true, "precision": 0, "correctAnswerStyle": "plain", "marks": 1, "type": "numberentry", "showPrecisionHint": false, "scripts": {}, "maxValue": "{ans1}"}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacements": [], "marks": 0, "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 $\\var{price[0]}$ pence per litre.</p>\n<p>&pound;[[0]]</p>", "type": "gapfill", "unitTests": [], "scripts": {}}], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}