Question

Note Use $\mathrm{\pi }=\frac{22}{7}$, unless stated otherwise.
The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Answer 1

Slant height, l = 14 cm

Let the radius of the base be r cm.

Curved surface area of the cone = 308 cm² (Given)

$$\begin{gathered} \therefore \mathrm{\pi }rl=308 \\ \Rightarrow \frac{22}{7}\times r\times 14=308 \\ \Rightarrow r=\frac{308\times 7}{22\times 14} \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$
∴ Total surface area of the cone = $\mathrm{\pi }r\left(r+l\right)=\frac{22}{7}\times 7\times \left(7+14\right)=\frac{22}{7}\times 7\times 21$ = 462 cm²

Thus, the radius of the base is 7 cm and the total surface area of the cone is 462 cm².