Question

The volume of a sphere is 4851 cm³. Find its curved surface area.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere}\mathrm{be}r. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere}=4851{\mathrm{cm}}^3 \\ \Rightarrow \frac{4}{3}\mathrm{\pi }{r}^3=4851 \\ \Rightarrow \frac{4}{3}\times \frac{22}{7}\times r^3=4851 \\ \Rightarrow r^3=4851\times \frac{3\times 7}{4\times 22} \\ \Rightarrow r^3=\frac{9261}{8} \\ \Rightarrow r=\sqrt[3]{\frac{9261}{8}} \\ \Rightarrow r=\frac{21}{2}\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sphere}=4\mathrm{\pi }{r}^2 \\ =4\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2} \\ =1386{\mathrm{cm}}^2 \end{gathered}$$

So, the curved surface area of the sphere is 1386 cm².