Question

The radius of sphere is 5 cm. If the radius is increased by 20$\%$, then find the percentage increase in the volume?

Answer 1

Given that the radius of the sphere is $5cm$.

Let the volume of the sphere be $V$.

We know that,

Volume of a sphere $=\frac{4}{3}\pi r^3\text{cubic units}$

$\therefore$ Volume $=\frac{4}{3}\pi \times 5^3$

$=\frac{4}{3}\pi \times 125$

$=\frac{500}{3}\pi c{m}^3$

Given that the radius is increased by $20\%$

$\therefore$ New radius $r^{\prime }=r+\frac{20}{100}r$

$\Rightarrow r+\frac{r}{5}$

$=\frac{6r}{5}=\frac{6}{5}\times 5$

$=6cm$

$\therefore$New volume $=\frac{4}{3}\pi \times 6\times 6\times 6$

$=8\times 36\pi$

$\Rightarrow 288\pi$

$\%\text{change}=\frac{\text{new volume}-\text{old volume}}{\text{old volume}}\times 100$

$\therefore \%\text{change}=\frac{288\pi -\frac{500}{3}\pi }{\frac{500}{3}\pi }\times 100$

$\Rightarrow \frac{864-500}{500}\times 100$

$\Rightarrow \frac{364}{500}\times 100=72.8\%$

Hence, if the radius of the sphere is increased by $20\%$, the volume will increase by $72.8\%$.