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Given the formula for a cone or a cylinder, and values for r and h, find the volume.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The formula for the volume of a {sel_solid} is {sel_formula}. 

", "advice": "

The volume is given by {sel_formula} where \\(r=\\var{r}\\) cm and \\(h=\\var{h}\\) cm.

\n

So volume $V=\\var{advice} \\approx \\var{answer}$ cm$^3$

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"solid": {"name": "solid", "group": "Ungrouped variables", "definition": "[\"cylinder\",\"cone\"]", "description": "", "templateType": "anything", "can_override": false}, "formula": {"name": "formula", "group": "Ungrouped variables", "definition": "[latex(\"V=\\\\pi r^2h\"),latex(\"V=\\\\frac13\\\\pi r^2h\")]", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "random(3..8)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "templateType": "anything", "can_override": false}, "selection": {"name": "selection", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "sel_solid": {"name": "sel_solid", "group": "Ungrouped variables", "definition": "solid[selection]", "description": "", "templateType": "anything", "can_override": false}, "sel_formula": {"name": "sel_formula", "group": "Ungrouped variables", "definition": "formula[selection]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "precround(eval(eval_formula[selection],[\"r\":r,\"h\":h]),0)", "description": "", "templateType": "anything", "can_override": false}, "eval_formula": {"name": "eval_formula", "group": "Ungrouped variables", "definition": "[expression(\"pi*r^2*h\"),expression(\"1/3*pi*r^2*h\")]", "description": "", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "latex(['','\\\\frac{1}{3}'][selection] + '\\\\pi*' + r+'^2' + '*' + h)", "description": "

latex([\"\",\"\\\\frac{1}{3}\"][selection]) + latex(\"\\\\pi\\\\times\") + latex(expression(r + \"^2\" + h))

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["solid", "formula", "r", "h", "selection", "sel_solid", "sel_formula", "answer", "eval_formula", "advice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find \\(V\\) when \\(r=\\var{r}\\) cm and \\(h=\\var{h}\\) cm. Give your answer correct to \\(0\\) decimal places.

\n

\\(V=\\)[[0]] cm\\(^3\\)

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