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{"name": "Kwame's copy of 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "metadata": {"description": "<p>Volume Problems</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Kwame's copy of Q6 Volume problems", "variables": {"size4": {"group": "Ungrouped variables", "name": "size4", "definition": "random(2..6 #0.5)", "templateType": "anything", "description": ""}, "ans2": {"group": "Ungrouped variables", "name": "ans2", "definition": "random(2.5..7#0.25)", "templateType": "anything", "description": ""}, "ans3": {"group": "Ungrouped variables", "name": "ans3", "definition": "(pi*((size3/2)^2)*size4)", "templateType": "anything", "description": ""}, "vol": {"group": "Ungrouped variables", "name": "vol", "definition": "precround((pi*((ans2)^2)*size1),2)", "templateType": "anything", "description": ""}, "ans2a": {"group": "Ungrouped variables", "name": "ans2a", "definition": "ans2*2", "templateType": "anything", "description": ""}, "size3": {"group": "Ungrouped variables", "name": "size3", "definition": "random(0.61..0.89#0.01  except 0.7 except 0.8)", "templateType": "anything", "description": ""}, "size1": {"group": "Ungrouped variables", "name": "size1", "definition": "random(3.25..6.25 #05)", "templateType": "anything", "description": ""}, "size2": {"group": "Ungrouped variables", "name": "size2", "definition": "shuffle(11..17#1)[0..5]", "templateType": "anything", "description": ""}, "ans1": {"group": "Ungrouped variables", "name": "ans1", "definition": "(2/3)*(pi*(((size2[0])/2)^3))", "templateType": "anything", "description": ""}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Solve the following volume questions to 2 decimal places.</p>", "tags": [], "preamble": {"css": "", "js": ""}, "parts": [{"showCorrectAnswer": true, "sortAnswers": false, "prompt": "<p><img src=\"resources/question-resources/hemisphere_31.png\"/></p>\n<p>Calculate the volume of a hemispherical container of&nbsp;diameter $\\var{size2[0]}$cm.</p>\n<p>[[0]]&nbsp;cm$^3$</p>", "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "marks": 1, "minValue": "{ans1}", "maxValue": "{ans1}", "precision": "2", "type": "numberentry", "showFeedbackIcon": true, "strictPrecision": false, "precisionPartialCredit": 0, "precisionType": "dp", "mustBeReducedPC": 0, "customName": "", "useCustomName": false}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacements": [], "useCustomName": false}, {"showCorrectAnswer": true, "sortAnswers": false, "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.</p>\n<p>[[0]]m</p>\n<p></p>", "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "marks": 1, "minValue": "{ans2a}", "maxValue": "{ans2a}", "precision": "2", "type": "numberentry", "showFeedbackIcon": true, "strictPrecision": false, "precisionPartialCredit": 0, "precisionType": "dp", "mustBeReducedPC": 0, "customName": "", "useCustomName": false}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacements": [], "useCustomName": false}, {"showCorrectAnswer": true, "sortAnswers": false, "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 $\\var{size3}$ m and a perpendicular height of&nbsp;$\\var{size4}$m.</p>\n<p>[[0]]&nbsp;m$^3$</p>", "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "marks": 1, "minValue": "{ans3}", "maxValue": "{ans3}", "precision": "2", "type": "numberentry", "showFeedbackIcon": true, "strictPrecision": false, "precisionPartialCredit": 0, "precisionType": "dp", "mustBeReducedPC": 0, "customName": "", "useCustomName": false}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacements": [], "useCustomName": false}], "rulesets": {}, "extensions": [], "ungrouped_variables": ["size1", "size2", "ans1", "ans2", "ans3", "vol", "size3", "size4", "ans2a"], "variable_groups": [], "advice": "<p>Part1</p>\n<p>Volume of hemispherical&nbsp;container</p>\n<p>V = $\\frac{4}{3}\\pi r^3$</p>\n<p>$\\frac{4}{3} \\times\\pi \\times (\\frac{\\var{size2[0]}}{2})^3 = \\var{precround(ans1,2)}$</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>=$2 \\times \\sqrt \\frac{\\var{vol}}{\\pi \\times \\var{size1}} = \\var{precround(ans2a,2)}$m</p>\n<p>Part3</p>\n<p>Volume of cylindrical container</p>\n<p>V = $\\pi r^2h$</p>\n<p>$\\pi \\times (\\frac{\\var{size3}}{2})^2 \\times \\var{size4} = \\var{precround(ans3,2)}$</p>", "contributors": [{"name": "Kwame D Dwamena", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/81/"}, {"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": "Kwame D Dwamena", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/81/"}, {"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/"}]}