Question

If the radius of the sphere is increased by $10$% prove that its volume will be increased by $33.1$% is

Answer 1

Let radius of sphere$=r$

Volume$=\frac{4}{3}\pi r^3$

Radius is increased by $10$ %$=r+\frac{10}{100}r$

$=r+\frac{r}{10}=\frac{11r}{10}$

Volume $=\frac{4}{3}\pi \times \frac{{11}^3}{1000}{r}^3$

Increased volume %$=\frac{(\frac{1331}{1000}-1)\frac{4}{3}\pi r^3}{\frac{4}{3}\pi r^3}\times 100$

$=\frac{331}{1000}\times 100=33.1$%

$\therefore$Volume increased by $33.1$%