Question

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. The number of balls formed is

(a) 16
(b) 32
(c) 24
(d) 28

Answer 1

(b) 32

Radius of the cone = 12 cm and its height = 24 cm
Volume of cone = $\frac{1}{3}\mathrm{\pi }{r}^2\mathrm{h}=\left(\frac{1}{3}\times \mathrm{\pi }\times 12\times 12\times 24\right){\mathrm{cm}}^2$
$=\left(48\times 24\right)\mathrm{\pi }{\mathrm{cm}}^2$
Volume of each ball = $\frac{4}{3}{\mathrm{\pi R}}^3=\frac{4}{3}\mathrm{\pi }\times 3\times 3\times 3$ [ Since diameter of each ball is 6 cm]
$=\left(36\mathrm{\pi }\right){\mathrm{cm}}^3$
Thus,
Number of balls formed = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{solid}\mathrm{cone}}{\mathrm{Volume}\mathrm{of}\mathrm{each}\mathrm{ball}}$
$=\frac{\left(48\times 24\mathrm{\pi }\right)}{36\mathrm{\pi }}=32$