Question

A solid metallic sphere of radius 8 cm is melted and recast into 64 identical solid spheres. The diameter of each smaller sphere formed is:

विकल्प

• 4 cm

• 2 cm

• 8 cm

• 1 cm

Answer 1

4 cm

Explanation:

Given,

Radius of larger metallic sphere (R) = 8 cm

Let radius of each smaller sphere be r cm.

Given,

A solid metallic sphere of radius 8 cm is melted and recast into 64 identical solid spheres.

∴ Volume of larger metallic sphere = 64 × Volume of smaller metallic sphere

\[\Rightarrow \frac{4}{3}\, \pi R^3 = 64 \times \frac{4}{3}\, \pi r^3\]

\[\Rightarrow 64 = \frac{\frac{4}{3}\, \pi R^3}{\frac{4}{3}\, \pi r^3}\]

\[\Rightarrow 64 = \frac{R^3}{r^3}\]

\[\Rightarrow 64 = \frac{8^3}{r^3}\]

\[\Rightarrow r^3 = \frac{8^3}{64}\]

\[\Rightarrow r^3 = \frac{512}{64}\]

\[\Rightarrow r^3 = 8\]

\[\Rightarrow r = \sqrt[3]{8} = 2\ \text{cm}.\]

Diameter of smaller sphere = 2 × 2 = 4 cm.