Question

A solid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is _________.

Answer 1

If a solid ball is exactly fitted inside the cuboidal box, then the diameter of the ball is equal to the side of the cuboidal box.

Let the radius of the ball be r units.

$$\begin{gathered} \therefore 2r=a \\ \Rightarrow r=\frac{a}{2} \end{gathered}$$

Volume of the ball = $=\frac{4}{3}\mathrm{\pi }{r}^3=\frac{4}{3}\mathrm{\pi }{\left(\frac{a}{2}\right)}^3=\frac{1}{6}\mathrm{\pi }{a}^3$

A solid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is $\underline{\frac{1}{6}\mathrm{\pi }{a}^3}$.