Geometry and TrigonometryVery hardVolume factor when a cone changes shape
Geometry and Trigonometry practice question
The radius of a cone is doubled and its height is halved. The new volume is how many times the original volume?
Answer: 2
Volume is proportional to r²h; doubling r multiplies it by 4 and halving h multiplies by 1/2: 4 × 1/2 = 2.
Common wrong answers
- If you answered 1
- 1 assumes doubling and halving cancel, but the radius is squared.
- If you answered 4
- 4 ignores the halved height.
- If you answered 8
- 8 treats the height as doubled too.
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