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"name": "size2", "definition": "shuffle(11..17#1)[0..5]"}, "size1": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "size1", "definition": "shuffle(7..10#1)[0..5]"}, "ans3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans3", "definition": "(4/3)*(pi*(((size1[2])/2)^3))"}}, "parts": [{"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>", "showFeedbackIcon": true, "variableReplacements": [], "stepsPenalty": 0, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans1}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans1}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "steps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "<p>The volume of a cylinder is given by $V=\\pi r^2h$ where $h$ is the height.</p>\n<p>Don't forget to use the radius rather than the diameter.</p>", "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information"}], "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"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>", "showFeedbackIcon": true, "variableReplacements": [], "stepsPenalty": 0, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans2}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans2}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "steps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "<p>The volume of a cone is given by $V=\\frac{1}{3}\\pi r^2h$ where $h$ is the perpendicular height.</p>", "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information"}], "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"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]]&nbsp;cm$^3$</p>", "showFeedbackIcon": true, "variableReplacements": [], "stepsPenalty": 0, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans3}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans3}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "steps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "<p>The volume of a sphere is given by $V=\\frac{4}{3}\\pi r^3$.</p>", "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information"}], "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Simon's copy of Q4 Calculating volume of different containers", "variable_groups": [], "functions": {}, "advice": "<p>Remember to convert diameter to radius by dividing by 2.</p>\n<p><strong>(a)</strong></p>\n<p>Volume of cylindrical container</p>\n<p>$V = \\pi r^2h$</p>\n<p>$\\pi \\times (\\frac{\\var{size1[0]}}{2})^2 \\times \\var{size2[0]} = \\var{precround(ans1,2)}$</p>\n<p><strong>(b)</strong></p>\n<p>Volume of conical&nbsp;container</p>\n<p>$V = \\frac{1}{3}\\pi r^2h$</p>\n<p>$\\frac{1}{3} \\times\\pi \\times (\\frac{\\var{size1[1]}}{2})^2 \\times \\var{size2[1]} = \\var{precround(ans2,2)}$</p>\n<p><strong>(c)</strong></p>\n<p>Volume of spherical&nbsp;container</p>\n<p>$V = \\frac{4}{3}\\pi r^3$</p>\n<p>$\\frac{4}{3} \\times\\pi \\times (\\frac{\\var{size1[2]}}{2})^3 = \\var{precround(ans3,2)}$</p>", "preamble": {"css": "", "js": ""}, "statement": "<p>Solve the following volume questions to 2 decimal places.</p>", "tags": [], "metadata": {"description": "<p>Calculating the volumes of different containers</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "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/"}], "resources": ["question-resources/1.png", "question-resources/charles1.1.gif", "question-resources/formula-explanation-sphere-1.jpg"]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": 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