Question

A sphere of radius 16 cm is melted and moulded to n spheres of radius 4 cm. Here, n =

• A. 16
• B. 4
• C. 64
• D. 32

Answer 1

The correct option is C 64

Given: Radius of bigger sphere, R = 16 cm
Radius of each small sphere, r = 4 cm

Let the number of small spheres formed be n.

Here, volume of bigger sphere = n $\times$ volume of small sphere

$\Rightarrow$ $\frac{4}{3}\pi R^3=n\times \frac{4}{3}\pi r^3$
$\Rightarrow$ $n=\frac{{16}^3}{4^3}$
$\Rightarrow$ $n=64$
$\therefore$ There will be 64 spheres of radius 4 cm.