Problem 13 · 2017 Math Kangaroo
Hard
Geometry & Measurement
proportion
Two cylinders A and B have the same volume. The radius of the base of B is 10% bigger than that of A. By how much is the height of A greater than that of B?
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Answer: E — 21%
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Hint 1 of 2
Equal volumes means (radius squared) x height is the same for both cylinders.
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Hint 2 of 2
If B's radius is 1.1 times A's, compare the heights through the square of that factor.
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Approach: use equal volume to relate the heights through the radius ratio
- Volume = pi r^2 h is equal, so r_A^2 h_A = r_B^2 h_B with r_B = 1.1 r_A.
- Then h_A = (r_B/r_A)^2 h_B = 1.21 h_B.
- So h_A is 21% greater than h_B.
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