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Question

A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the
diameter of the sphere. [CBSE 2014]

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Solution

We have,Height of the cone, h=84 cm andBase radius of the cone, r=21 cmLet the radius of the solid sphere be R.Now,Volume of the solid sphere=Volume of the solid cone43πR3=13πr2hR3=r2h4R3=21×21×844R3=21×21×21R=21 cm Diameter=2R=2×21=42 cm

So, the diameter of the solid sphere is 42 cm.

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