Volume scale factors
Objective. Connect volume scale factor to the cube of the linear factor.
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- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The volume scale factor between two similar solids equals the cube of the linear scale factor, since volume depends on three dimensions multiplied together. If the linear scale factor is k, then corresponding volumes are related by a factor of k³. For example, if a model is enlarged with a linear scale factor of 2, its volume becomes 2³ = 8 times larger. To reverse this process and find the linear scale factor from a known volume ratio, take the cube root of the volume scale factor.
Worked example
Two similar solids have a linear scale factor of 3. If the smaller solid has a volume of 20 cm³, find the volume of the larger solid.
- 1The volume scale factor equals the linear scale factor cubed: 3³ = 27.
- 2Multiply the smaller solid's volume by this volume scale factor.
- 320 × 27 = 540.
- 4The larger solid's volume is therefore 540 cm³.
Answer: 540 cm³
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often use the square of the linear scale factor for volume, confusing it with the area scale factor rule, giving an answer that is far too small. Always cube the linear scale factor, not square it, when scaling volumes.
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