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Volume of a solid

A copper sphe...

Question

A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone.

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Solution

The radius of the copper sphere is 3cm. Therefore, the volume of the copper sphere is

The copper sphere is melted to produce a right circular cone. The height of the right circular cone is 3cm. Let the base-radius of the right circular cone is r. Then, the volume of the right circular cone is

Since, the sphere is melted to recast the cone; the volumes of the sphere and the cone are equal. Hence, we have

Hence, the base-radius of the right circular cone is 6 cm.

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