Question

The volume of a right circular cone of height 24 cm is 1232 cm³. Its curved surface area is
(a) 1254 cm²
(b) 704 cm²
(c) 550 cm²
(d) 462 cm²

Answer 1

(c) 550 cm²
Let r cm be the radius of the cone.
Volume of the right circular cone = 1232 cm³
Then we have:
$$\begin{gathered} \frac{1}{3}\times \frac{22}{7}\times r^2\times 24=1232 \\ \Rightarrow r^2=\frac{1232\times 21}{22\times 24} \\ \Rightarrow r^2=49 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cone}=\mathrm{\pi }rl \\ =\frac{22}{7}\times 7\times \sqrt{7^2+{24}^2} \\ =22\times \sqrt{49+576} \\ =22\times 25 \\ =550{\mathrm{cm}}^2 \end{gathered}$$