Question

If the total surface area of a solid hemisphere is 462 cm², then find its volume. [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{hemisphere}=462{\mathrm{cm}}^2 \\ \Rightarrow 3\mathrm{\pi }{r}^2=462 \\ \Rightarrow 3\times \frac{22}{7}\times r^2=462 \\ \Rightarrow r^2=\frac{462\times 7}{3\times 22} \\ \Rightarrow r^2=49 \\ \Rightarrow r^2=\sqrt{49} \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Now},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{hemisphere}=\frac{2}{3}\mathrm{\pi }{r}^3 \\ =\frac{2}{3}\times \frac{22}{7}\times 7\times 7\times 7 \\ =\frac{2156}{3}{\mathrm{cm}}^3 \\ =718\frac{2}{3}{\mathrm{cm}}^3 \end{gathered}$$
= 718.67 cm³