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Question

# A solid metallic right circular cylinder and a solid metallic right circular cone are given. The cylinder and cone both have same height h and same base radii r. The two solids are melted together and recast into a solid cylinder of radius 12r. Then the height of the cylinder is 163h.

A
True
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B
False
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Solution

## The correct option is A TrueVolume of the resulting cylinder = Volume of Cylinder + Volume of Cone which are melted. Let the height of the resulting cylinder be H. Volume of a cone =13πr2h, where r is the radius of the base of the cone and h is the height.Volume of a cylinder of radius R and height h, =πR2hSo, π(r2)2H=πr2h+13πr2h⇒H4=43h⇒H=163hHence, the height of the resulting cylinder is 163h.

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