Question

A solid ball is exactly fitted inside the cubical box of side $a$. The volume of the ball is $\frac{4}{3}\pi a^3$. Write ‘True’ or ‘False’ and justify your answer

• A. True
• B. False

Answer 1

The correct option is B False

Verify the given statement:

Given that the cubical box is of side $a$

Since, the spherical ball is exactly fitted inside the cube, the diameter of the ball is equal to the side of the cube

Let $d$ be the diameter of the spherical ball and $r$ be the radius.

$\therefore$ $a=d$ and $d=2r$

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

The volume of a sphere is given as

$V=\frac{4}{3}{\mathrm{\pi r}}^3$

$\Rightarrow$$V=\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3$

$\Rightarrow$$V=\frac{1}{6}\pi a^3$$\ne \frac{4}{3}\pi a^3$

Hence, the given statement is false.