Exams › SSC CGL (Prelims) › General

A cone and a hemisphere have the same radius. Their combined height is 24 cm. If both have equal volumes, find the radius.

1. 8 cm
2. 9 cm
3. 10 cm
4. 12 cm

Correct answer: 8 cm

Solution

Let the common radius be r. The hemisphere’s height is r, so the cone’s height is 24 - r. Since their volumes are equal, \(\frac{1}{3}\pi r^2(24-r)=\frac{2}{3}\pi r^3\). Solving gives r = 8 cm.

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