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 balls obtained.

Answer 1

Radius of solid sphere = 3 cm
Volume of the sphere$=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\times 3\times 3\times 3{\mathrm{cm}}^3$

Radius of each new ball = 0.3 cm
Volume of each new ball $=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}{\mathrm{cm}}^3$

Total number of balls $=\frac{\frac{4}{3}\mathrm{\pi }\times 3\times 3\times 3}{\frac{4}{3}\mathrm{\pi }\times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}}=1000$