The radii of two cones are in the ratio 2:1, their volumes are equal. Find the ratio of their heights.
(A) 1:8
(B) 1:4
(C) 2:1
(D) 4:1


Answer: (B)

Explanation: Let the radius and height of the two cones be R, H and r, h respectively such that R:r = 2:1. Then,
Volume of the cone C = 1/3 * π * R² * H
Volume of the cone c = 1/3 * π * r² * h
Now,
1/3 * π * R² * H = 1/3 * π * r² * h
H:h = r²:R² = 1²:2² = 1:4.

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