Question

The volume of a hemisphere is cm³. Find its curved surface area. [CBSE 2012]

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{volume}\mathrm{of}\mathrm{hemisphere}=2425\frac{1}{2}{\mathrm{cm}}^3 \\ \Rightarrow \frac{2}{3}\mathrm{\pi }{r}^3=2425\frac{1}{2} \\ \Rightarrow \frac{2}{3}\times \frac{22}{7}\times r^3=\frac{4851}{2} \\ \Rightarrow r^3=\frac{4851\times 3\times 7}{2\times 2\times 22} \\ \Rightarrow r^3=\frac{441\times 3\times 7}{2\times 2\times 2} \\ \Rightarrow r^3=\frac{{21}^3}{2^3} \\ \Rightarrow r=\frac{21}{2}\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{So},\mathrm{the}\mathrm{curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{hemisphere}=2\mathrm{\pi }{r}^2 \\ =2\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2} \\ =693{\mathrm{cm}}^2 \end{gathered}$$