// Numbas version: exam_results_page_options
{"name": "Calculate density given mass and volume", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<h4>a)</h4>\n<p>We are told that the ball has a volume of $\\var{volume}\\text{cm}^3$ and a mass of $\\var{mass}$g, and we are asked to calculate the density of the box in g/cm$^3$.</p>\n<p>The formula for density is</p>\n<p>\\[\\begin{align} \\text{Density} &amp;= \\frac{\\text{Mass}}{\\text{Volume}} \\\\[4pt]<br/>&amp;= \\frac{\\var{mass}}{\\var{volume}} \\\\[4pt]<br/>&amp;= \\var{density} \\\\<br/>&amp;= \\var{precround(density,2)}\\text{g/cm}^3\\text{.} \\\\<br/>\\end{align}\\]</p>\n<h4>b)</h4>\n<p>Since the density of the ball is {if(density&gt;1,'greater','smaller')} than the density of water, {person['name']}'s ball will&nbsp;{if(density&gt;1,'sink','float')}.</p>\n<p></p>", "statement": "<p>A solid object placed in water will sink if its density is greater than that of water ($1\\text{g/cm}^3$).</p>\n<p>{person['name']}'s toy ball has a volume of $\\var{volume}\\text{cm}^3$&nbsp;and a mass of $\\var{mass}$g. Whilst playing, {person['pronouns']['they']} drops&nbsp;{person['pronouns']['their']} ball into a pond.</p>", "variables": {"mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(55..65)", "templateType": "anything", "description": "<p>mass of the box</p>"}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "templateType": "anything", "description": ""}, "density": {"name": "density", "group": "Ungrouped variables", "definition": "mass/volume", "templateType": "anything", "description": ""}, "volume": {"name": "volume", "group": "Ungrouped variables", "definition": "random(40..70 except mass)", "templateType": "anything", "description": "<p>Volume of box</p>"}, "mark_matrix": {"name": "mark_matrix", "group": "Ungrouped variables", "definition": "[if(density<1,1,0),if(density>1,1,0)]", "templateType": "anything", "description": ""}}, "tags": ["calculating density", "compound units", "Compound units", "density", "mass", "taxonomy", "Volume", "volume"], "ungrouped_variables": ["volume", "mass", "density", "person", "mark_matrix"], "functions": {}, "name": "Calculate density given mass and volume", "metadata": {"description": "<p>Calculate the density of an object given its mass and volume.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": ["random_person"], "parts": [{"scripts": {}, "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>The&nbsp;relationship between density, mass and volume is</p>\n<p>\\[\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}}.\\]</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "precisionPartialCredit": 0, "strictPrecision": false, "correctAnswerFraction": false, "minValue": "density", "allowFractions": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "scripts": {}, "maxValue": "density", "showCorrectAnswer": true, "precision": "2", "type": "numberentry", "showPrecisionHint": false, "marks": 1, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "precisionMessage": "<p>Round your answer to $3$ significant figures.</p>"}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>What is the density of the ball?&nbsp;</p>\n<p>[[0]] g/cm$^3$. &nbsp; &nbsp; &nbsp;<em><small>Round your answer to $2$&nbsp;decimal places.</small></em></p>", "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"variableReplacements": [], "maxMarks": 0, "displayType": "radiogroup", "choices": ["<p>It&nbsp;floats</p>", "<p>It sinks</p>"], "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "shuffleChoices": false, "prompt": "<p>Does {person['name']}'s ball float or sink?</p>", "marks": 0, "showFeedbackIcon": true, "matrix": "mark_matrix", "variableReplacementStrategy": "originalfirst", "minMarks": 0}], "type": "question", "variable_groups": [], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}]}], "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}