Question

The volume of a hemi-sphere is 2425$\frac{1}{2}$ cm³. Find its curved surface area. (Use π = 22/7)

Answer 1

Let the radius of the hemisphere be r cm.
Volume of hemisphere = $2425\frac{1}{2}{\mathrm{cm}}^3$
$$\begin{gathered} \Rightarrow \frac{2}{3}\mathrm{\pi }{r}^3=\frac{4851}{2} \\ \Rightarrow \frac{2}{3}\times \frac{22}{7}{r}^3=\frac{4851}{2} \\ \Rightarrow r^3=\frac{4851\times 3\times 7}{2\times 2\times 22} \\ \Rightarrow r^3=\frac{441\times 21}{2\times 2\times 2} \\ \Rightarrow r^3={\left(\frac{21}{2}\right)}^3 \\ \Rightarrow r=\frac{21}{2}\mathrm{cm} \end{gathered}$$
Now, the curved surface area of hemisphere is given by
$$\begin{gathered} 2\mathrm{\pi }{r}^2 \\ =2\times \frac{22}{7}\times {\left(\frac{21}{2}\right)}^2 \\ =693{\mathrm{cm}}^2 \end{gathered}$$