Density in compound solids
Objective. Combine volume, mass and unit conversion accurately.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Density in compound solids combines volume calculations for composite shapes with the formula density = mass ÷ volume, then requires careful unit conversion. First split the compound solid into simple parts (cuboids, cylinders, cones etc.), find the total volume, then use mass = density × volume or rearrange as needed. Units must match, so cm³ pairs with g/cm³ and must be converted consistently if the problem mixes metres and centimetres. For a solid of volume 50 cm³ with density 7.8 g/cm³, mass = 50 × 7.8 = 390 g. Always state final units clearly, since examiners penalise missing or wrong units here.
Worked example
A compound solid has total volume 120 cm³ and density 2.5 g/cm³. Find its mass.
- 1Use mass = density × volume
- 2Mass = 2.5 × 120
- 3Mass = 300
- 4Mass = 300 g
Answer: 300 g
Concept mastery
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Practice
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Start practisingCommon mistake. A classic slip is multiplying density by a volume still in different units, such as using a volume in m³ with a density in g/cm³, producing an answer wildly out of scale. Convert everything to consistent units first.
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