Geometry and TrigonometryHardVolume ratio when dimensions change
Geometry and Trigonometry practice question
A cylinder has radius r and height h. A second cylinder has radius 2r and height h/2. The volume of the second cylinder is how many times the volume of the first?
- A. 2Correct
- B. 4
- C. 1
- D. 8
Answer: A. 2
V = πr²h. Doubling the radius multiplies r² by 4; halving the height multiplies by 1/2. Net factor: 4 × 1/2 = 2.
Why the other answers are wrong
- B. 4
- 4 accounts for the radius doubling (r² → 4r²) but ignores the height being halved.
- C. 1
- 1 assumes doubling and halving cancel. They don't, because the radius is SQUARED: 4 × 1/2 = 2.
- D. 8
- 8 would be the factor if all three dimensions doubled. Here the height is halved.
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