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{"name": "Volume and Surface Area of Sphere", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["rord", "r", "a", "vol", "sa"], "name": "Volume and Surface Area of Sphere", "tags": ["sphere", "surface area", "volume"], "preamble": {"css": "", "js": ""}, "advice": "<p>Recall that the volume, $V$, of a sphere is given by the formula $ V = \\dfrac { 4}{3}\\pi r^3$ where $r$ is the <strong>radius</strong>.</p>\n<p>The surface area, $S$, is given by $S = 4 \\pi r^2$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>Volume is&nbsp; [[0]] cm<sup>3&nbsp;</sup> </p>\n<p><sup></sup></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "maxValue": "{vol}", "minValue": "{vol}", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Surface area is&nbsp; [[0]]&nbsp; cm<sup>2</sup></p>\n<p><sup></sup></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "maxValue": "{sa}", "minValue": "{sa}", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>A sphere has a {rord} of {a} cm.</p>\n<p>Find its volume and surface area, rounding your answers to 1 d. p.</p>\n<p><em>Use the $\\pi$ button on your calculator or the value&nbsp; $\\pi= 3.142$</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "variables": {"a": {"definition": "random(2..15 #0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "vol": {"definition": "pi*4/3*r^3", "templateType": "anything", "group": "Ungrouped variables", "name": "vol", "description": ""}, "sa": {"definition": "pi*4*r^2", "templateType": "anything", "group": "Ungrouped variables", "name": "sa", "description": ""}, "r": {"definition": "If(rord= 'radius', a, a/2)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "rord": {"definition": "random('radius', 'diameter')", "templateType": "anything", "group": "Ungrouped variables", "name": "rord", "description": ""}}, "metadata": {"description": "<p>Recall and use of formulae for volume and surface area of a sphere.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}]}]}], "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}]}