Given: The radii of two cones of copper and aluminium are in the ratio of 3:7, consider their volumes to be equal. Find the ratio of their heights.
(A)
9:49
(B)
3:7
(C)
49:9
(D)
7:3
Answer: (C)
Explanation:
Let the radius and height of the two cones be R, H and r, h respectively such that R:r = 3:7. 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 = 7²:3² = 49:9.
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