Question

A solid sphere of radius 3 cm is melted and then cast into small spherical balls, each of diameter 0.6 cm. Find the number of small balls so obtained.

Answer 1

Radius of sphere = 3 cm

Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \pi \times 3\times 3\times 3c{m}^3=36\pi c{m}^3$

Radius of small sphere = 0.62 cm = 0.3 cm

Volume of small sphere $=\frac{4}{3}\times \pi \times 0.3\times 0.3\times 0.3c{m}^3=\frac{4}{3}\pi \times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}c{m}^3$

Let the number of small balls be n

$n\times \frac{4}{3}\pi \times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}=\frac{4}{3}\times \pi \times 3\times 3\times 3n=1000$

Hence, the number of small balls = 1000.