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{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["size1", "size2", "ans1", "ans2", "ans3"], "name": "Q4 Calculating volume of different containers", "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"}], "extensions": [], "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": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}