If the radius of a sphere is increased by P% , then find the value of increase in it surface area.

Let the initial radius be r .
when it is raised by P% , new raius will be r + rP/100 .
Initially its surface area was
$$\begin{gathered} = 4{\mathrm{\pi r}}^{2 } \\ \mathrm{Now} \mathrm{the} \mathrm{surface} \mathrm{area} \mathrm{will} \mathrm{be} 4\mathrm{\pi }(\mathrm{r}+ \frac{\mathrm{Pr}}{100}{)}^2. \\ \mathrm{Surface} \mathrm{area} \mathrm{is} \mathrm{increased} \mathrm{by} 4\mathrm{\pi }(\mathrm{r}+ \frac{\mathrm{Pr}}{100}{)}^2 - 4{\mathrm{\pi r}}^{2 } \\ = 4{\mathrm{\pi r}}^2(1+\frac{\mathrm{P}}{100}{)}^2- 4{\mathrm{\pi r}}^{2 } \\ = 4{\mathrm{\pi r}}^{2 }\times (\frac{{\mathrm{P}}^2}{10000} + \frac{2\mathrm{P}}{100}) \\ \mathrm{Hope} \mathrm{this} \mathrm{would} \mathrm{have} \mathrm{cleared} \mathrm{your} \mathrm{doubt} . \end{gathered}$$