Exams › SSC CGL (Prelims) › General

A sphere and a cone have the same volume and the same base radius. Find the ratio of the height of the cone to its radius.

1. 2:1
2. 3:1
3. 4:1
4. 8:1

Correct answer: 4:1

Solution

Volume of sphere = \(\frac{4}{3}\pi r^3\) and volume of cone = \(\frac{1}{3}\pi r^2 h\). Since they are equal and have the same radius, \(\frac{1}{3}\pi r^2 h = \frac{4}{3}\pi r^3\), giving \(h = 4r\). Hence the ratio of height to radius is 4:1.

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