Question

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is
(1) 3xcm (2) xcm (3) 4xcm (4) 2xcm

Answer 1

Let the height of the cone is h 

Volume remains constant.

Therefore, volume of cone = volume of sphere

$\frac{1}{3} \pi {r}^{2}h = \frac{4}{3} \pi {r}^{3} \\ \\ {x}^{2}h \: = 4 {x}^{3} \\ \\ h = 4x$

Answer 2

Let the height of the cone is h 

Volume remains constant.

Therefore, volume of cone = volume of sphere

1/3 πr^2h = 4/3 π R^3

x^2 h = 4 x^3

h = 4 x

hope it helps

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