// 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

#### a)

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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$^3$.

\n

The formula for density is

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\\\begin{align} \\text{Density} &= \\frac{\\text{Mass}}{\\text{Volume}} \\\\[4pt] &= \\frac{\\var{mass}}{\\var{volume}} \\\\[4pt] &= \\var{density} \\\\ &= \\var{precround(density,2)}\\text{g/cm}^3\\text{.} \\\\ \\end{align}\

\n

#### b)

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Since the density of the ball is {if(density>1,'greater','smaller')} than the density of water, {person['name']}'s ball will {if(density>1,'sink','float')}.

\n

", "statement": "

A solid object placed in water will sink if its density is greater than that of water ($1\\text{g/cm}^3$).

\n

{person['name']}'s toy ball has a volume of $\\var{volume}\\text{cm}^3$ and a mass of $\\var{mass}$g. Whilst playing, {person['pronouns']['they']} drops {person['pronouns']['their']} ball into a pond.

", "variables": {"mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(55..65)", "templateType": "anything", "description": "

mass of the box

"}, "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": "

Volume of box

"}, "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": "

Calculate the density of an object given its mass and volume.

", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": ["random_person"], "parts": [{"scripts": {}, "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "

The relationship between density, mass and volume is

\n

\$\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}}.\$

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Round your answer to $3$ significant figures.

"}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "prompt": "

What is the density of the ball?

\n

[[0]] g/cm$^3$.      Round your answer to $2$ decimal places.

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It floats

", "

It sinks

"], "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "shuffleChoices": false, "prompt": "

Does {person['name']}'s ball float or sink?

", "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/"}]}