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

(B) False.
Since the solid ball is exactly fitted inside the cubical box of side $a$,the diameter of the ball must be equal to the side of the cube,which is $a$.
Therefore,the radius of the ball $r = \frac{a}{2}$.
The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^{3}$.
Substituting $r = \frac{a}{2}$ into the formula,we get:
$V = \frac{4}{3} \pi \left( \frac{a}{2} \right)^{3} = \frac{4}{3} \pi \left( \frac{a^{3}}{8} \right) = \frac{1}{6} \pi a^{3}$.
Since $\frac{1}{6} \pi a^{3} \neq \frac{4}{3} \pi a^{3}$,the given statement is False.