Question

The curved surface area of a sphere is 5544 cm². Find its volume.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere}\mathrm{be}r. \\ \mathrm{As}, \\ \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sphere}=5544{\mathrm{cm}}^2 \\ \Rightarrow 4\mathrm{\pi }{r}^2=5544 \\ \Rightarrow 4\times \frac{22}{7}\times r^2=5544 \\ \Rightarrow r^2=5544\times \frac{7}{4\times 22} \\ \Rightarrow r^2=441 \\ \Rightarrow r=\sqrt{441} \\ \Rightarrow r=21\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere}=\frac{4}{3}\mathrm{\pi }{r}^3 \\ =\frac{4}{3}\times \frac{22}{7}\times 21\times 21\times 21 \\ =38808{\mathrm{cm}}^3 \end{gathered}$$

So, the volume of the sphere is 38808 cm³.