Question

A sphere of diameter 14 CM is melted and recasted in the small spheres of each radius 1cm . Then find the number of small spheres.

Answer 1

Diameter of big sphere = 14 cm

Radius of big sphere, R = 14 / 2 = 7 cm

Radius of small sphere, r = 1 cm

Let the number of small spheres formed be n .

So,

Volume of big sphere = n × Volume of small spheres

$\frac{4}{3}\pi R^3=n(\frac{4}{3}\pi r^3)$

4/3 and π gets cancelled .

$(7)^3=n[(1)^3]\\\\343 = n$

Hence , 343 small spheres with radius 1 cm can be formed by melting a big sphere of radius 7 cm.