Question

A solid metallic sphere of radius 16 cm is melted to form small identical spheres each of diameter 4 cm. The number of spheres formed is:

Options

• 64

• 252

• 512

• 1024

Answer 1

512

Explanation:

Given,

A solid metallic sphere of radius \[16\ \text{cm}\] is melted to form small identical spheres each of diameter \[4\ \text{cm}.\]

Larger metallic ball sphere radius \[(R) = 16\ \text{cm}\]

Radius of smaller metallic sphere \[(r) = \frac{4}{2} = 2\ \text{cm}\]

Let no. of smaller spheres formed be \[n.\]

∴ Volume of larger metallic ball = \[n\] × Volume of smaller metallic ball

\[\Rightarrow \frac{4}{3}\, \pi R^3 = n \times \frac{4}{3}\, \pi r^3\]

\[\Rightarrow n = \frac{\frac{4}{3}\, \pi R^3}{\frac{4}{3}\, \pi r^3}\]

\[\Rightarrow n = \frac{R^3}{r^3}\]

\[\Rightarrow n = \frac{16^3}{2^3}\]

\[\Rightarrow n = \frac{4096}{8} = 512.\]