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Question

State True or False:The radius of a solid metallic sphere is r. A solid metallic cone of height h has a base radius r. The two are melted together and recast into a solid right circular cone with a base radius r. Then, the height of the resulting cone is 4r+h.

A
True
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B
False
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Solution

The correct option is A TrueVolume of resulting cone = Volume of sphere + Volume of cone which are melted. Volume of a sphere of radius 'r' =43πr3Volume of a cone =13πr2h, wherer is the radius of the base of the cone and h is the height.Let the height of the resulting cone be HHence, 13πr2H=43πr3+13πr2h⇒H=4r+hHence, height of the resulting cone is 4r+h.

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