# A hollow sphere of external and internal diameters of 8 cm and 4 cm respectively is melted and made into another solid in the shape of a right circular cone of base diameter of 8 cm. find the height of the cone.

Voume of hollow sphere= $\frac{4}{3}*\prod *(r_{0}^{3}-r_i^{3}) \; \; \; where\; r_{0} \; is \;external \; radius, \;r_{i} \;is \;inner \; radius$

Voume of hollow sphere=$\frac{4}{3}*\prod *(4^{3}-2^{3}) \; \; \; equation(1)$

Voume of right circular cone=$\frac{1}{3}*\prod *r^{2}*h \; \; \; \; where \; r \; is \; radius \; of \; cone \; and \; h \; is\; height\; of\; cone\;$

Voume of right circular cone=$\frac{1}{3}*\prod *4^{2}*h \; \; \; \; \; \; \; equation(2)$

From equation(1) and equation(2)

$\frac{4}{3}*\prod *(4^{3}-2^{3})=\frac{1}{3}*\prod*4^{2}*h$

$\Rightarrow 4 *(4^{3}-2^{3})=16*h$

$\Rightarrow 64-8=4*h$

$\Rightarrow 56=4*h$

$\Rightarrow h=14$

Height of cone is 14 cm

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