Question

A solid ball is exactly fitted inside the cubical box of side a. Find the volume of the ball.

Answer 1

Given the solid ball is exactly fitted into cubical box of side a

Therefore the radius of the solid ball is exactly half of the side of the cubical box

$\therefore r=\frac{a}{2}$

Volume of solid ball $=\frac{4}{3}.\pi .r^3=\frac{4}{3}.\pi .\frac{a^3}{8}$

$\therefore$ Volume of solid ball $=\frac{\pi a^3}{6}$