Question

How many solid spheres of radius 1 cm will be formed by melting a solid metallic sphere of radius 8 cm?

Answer 1

Radius of the solid metallic sphere = 8 cm
Volume = $\frac{4}{3}\mathrm{\pi }{r}^3$
⇒ Volume = $\frac{4}{3}\mathrm{\pi }\times 8^3{\mathrm{cm}}^3$
This volume will be equal to the volume of all the solid spheres of radius 1 cm each that will be formed.
Radius of the small spheres = 1 cm
Let the number of such spheres be n.
So, n × $\frac{4}{3}\mathrm{\pi }\times 1^3=\frac{4}{3}\mathrm{\pi }\times 8^3$
⇒ n = 512