Question

The surface area of a sphere is 2464 cm². If its radius be doubled, then what will be the surface area of the new sphere?

Answer 1

Let the radii of the given sphere and the new sphere be r and R, respectively.

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ R=2r\mathrm{and}\mathrm{the}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{sphere}=2464{\mathrm{cm}}^2 \\ \mathrm{i}.\mathrm{e}.\mathit{}4\mathrm{\pi }{r}^{\mathit{2}}=2464{\mathrm{cm}}^2 \\ \mathrm{The}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}=4\mathrm{\pi }{R}^2 \\ =4\mathrm{\pi }{\left(2r\right)}^2 \\ =4\mathrm{\pi }\left(4r^2\right) \\ =4\left(\mathit{4}\pi r^{\mathit{2}}\right) \\ =4\times 2464 \\ =9856{\mathrm{cm}}^2 \end{gathered}$$

So, the surface area of the new sphere is 9856 cm².