Question

The radius and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm², find its radius.

Answer 1

Suppose, the radius and slant height of the cone are 4x cm and 7x cm.
Curved surface are of the cone = 792 cm²
$$\begin{gathered} \Rightarrow \mathrm{\pi }rl=792 \\ \Rightarrow \frac{22}{7}\times 4x\times 7x=792 \\ \Rightarrow 88x^2=792 \\ \Rightarrow x^2=9 \\ \Rightarrow x=3 \end{gathered}$$
Hence, radius of the cone = 4x = 4$\times$3 = 12 cm