Geometry and TrigonometryVery hardEffect of scaling on volume
Geometry and Trigonometry practice question
A sculptor makes a small clay model of a statue and then a full-size version that is 4 times as tall, with the same shape. The model uses 2 kilograms of clay. How much clay does the full-size statue use?
- A. 128 kgCorrect
- B. 8 kg
- C. 32 kg
- D. 64 kg
Answer: A. 128 kg
Volume scales with the cube of the length factor: 4³ = 64, so 2 × 64 = 128 kg.
Why the other answers are wrong
- B. 8 kg
- 8 kg scales by 4, as if clay scaled with height alone.
- C. 32 kg
- 32 kg scales by 4² = 16, which is how AREA scales.
- D. 64 kg
- 64 kg is the scale factor 4³ alone, forgetting the model's 2 kg.
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