Question

The volume of a right circular cone of height 24 cm is 1232 cm³. Find its curved surface area.

Answer 1

Height of the cone = 24 cm
$$\begin{gathered} \mathrm{Volume}\mathrm{of}\text{the}\mathrm{cone}=1232{\mathrm{cm}}^3 \\ \Rightarrow \frac{1}{3}\mathrm{\pi }{r}^{2}h=1232 \\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times r^2\times 24=1232 \\ \Rightarrow r^2=\frac{1232\times 3\times 7}{22\times 24} \\ \Rightarrow r^2=49 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\text{the}\mathrm{cone}=\mathrm{\pi }rl \\ =\frac{22}{7}\times 7\times \sqrt{7^2+{24}^2}\left(l=\sqrt{r^2+h^2}\right) \\ =22\times \sqrt{625} \\ =22\times 25 \\ =550{\mathrm{cm}}^2 \end{gathered}$$