Exams › SSC CGL (Prelims) › General

A right circular cone has the same volume as a sphere. If the cone's height is four times its base radius, find the ratio of the cone's radius to the sphere's radius.

1. 1:1
2. cbrt(3) : 1
3. 1 : cbrt(2)
4. cbrt(4) : 1

Correct answer: 1:1

Solution

With h = 4r, the cone's volume is (1/3)*pi*r^2*4r = (4/3)*pi*r^3, which is identical in form to the sphere's volume (4/3)*pi*R^3. Equating gives r^3 = R^3, so r = R and the ratio is 1:1.

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