Question

If the volume of a solid sphere is $7241\frac{1}{7}cu.cm$, then find its radius. $(Take\pi =\frac{22}{7})$

Answer 1

Let $r$ and $V$ be the radius and volume of the solid sphere respectively.
Given that $V=7241\frac{1}{7}=\frac{7241\times 7+1}{7}cu.cm$
$\Rightarrow \frac{4}{3}\pi r^3=\frac{50688}{7}$
$\Rightarrow \frac{4}{3}\times \frac{22}{7}\times r^3=\frac{50688}{7}$
$\Rightarrow r^3=\frac{50688}{7}\times \frac{3\times 7}{4\times 22}$
$=1728=4^3\times 3^3$
$\Rightarrow r=3\sqrt{4^3\times 3^3}$
$=4\times 3=12$
Thus, the radius of the sphere, $r=12cm$.