Calculate density
Calculate density using supplied evidence and a solved model.
About 25 minutes, plus any extended practice
Supplied materials
- All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
- Paper or browser document; an ordinary calculator is optional.
- Rule: Density equals mass in grams divided by volume in cubic centimeters. Formula: a/b. Variable key: a = mass (g), b = volume (cm³)
- Distinct worked inputs and result: A distinct sample has 35 g mass and 5 cm³ volume: 35/5=7 g/cm³.
- Assessment case 1: Supplied case 1: mass (g)=24; volume (cm³)=8, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
- Assessment case 2: Supplied case 2: mass (g)=40; volume (cm³)=10, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
- Assessment case 3: Supplied case 3: mass (g)=54; volume (cm³)=18, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
- Assessment case 4: Supplied case 4: mass (g)=60; volume (cm³)=12, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
- Assessment case 5: Supplied case 5: mass (g)=72; volume (cm³)=24, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
- Assessment case 6: Supplied case 6: mass (g)=84; volume (cm³)=14, using the explicitly named quantities. Density equals mass in grams divided by volume in cubic centimeters. What result follows?
Learn the idea
Density is mass per volume, not mass alone. Use a homogeneous sample and matched units. Two differently sized pieces of the same uniform material can have the same density.
Density equals mass in grams divided by volume in cubic centimeters. The formula in the supplied model is a/b. Variable key: a = mass (g), b = volume (cm³). Density compares mass with volume. Use sample mass and sample volume together.
A distinct sample has 35 g mass and 5 cm³ volume: 35/5=7 g/cm³. A larger sample need not be denser. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.
- Name the measured quantities and their units before substituting values.
- Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
- Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
- Explain the result in context and identify the assumption that would invalidate direct use of the rule.
See the method in action
Worked distinct example: A distinct sample has 35 g mass and 5 cm³ volume: 35/5=7 g/cm³. Method: identify the quantities in the stated rule, substitute using compatible units, and perform the operations in the correct order. Density compares mass with volume. Use sample mass and sample volume together. Interpret the final unit and keep the model assumption visible; this calculation is not a measurement of a real learner or site.
Check your reasoning
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Helpful tips
- Density compares mass with volume.
- Use sample mass and sample volume together.
See the answer and explanation
3 g/cm³
Substitute the supplied values: (24)/(8) = 3 g/cm³. Density compares mass with volume. A larger sample need not be denser.
Take it further
Changed-input task: use the same stated model with mass (g)=25; volume (cm³)=8. Expected result: 3.125 g/cm³. Explain what changes and keep this assumption: A larger sample need not be denser.
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More practice: try new cases
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Check the subject sources
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