Question

If the total surface area of a solid hemisphere is 462 cm², find its volume (Take π = 22/7 ) [CBSE 2014]

Answer 1

Let the radius of the hemisphere be r cm.
Total surface area of hemisphere = 462 cm²
$$\begin{gathered} \Rightarrow 3\mathrm{\pi }{r}^2=462 \\ \Rightarrow 3\times \frac{22}{7}\times {\left(r\right)}^2=462 \\ \Rightarrow r^2=49 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$
Now, the volume of hemisphere is given by
$$\begin{gathered} \frac{2}{3}\mathrm{\pi }{r}^3 \\ =\frac{2}{3}\times \frac{22}{7}{\left(7\right)}^3 \\ =\frac{2156}{3} \\ =718\frac{2}{3}{\mathrm{cm}}^3 \end{gathered}$$