Question

# The area of the curved surface of a cone is $60\pi {\text{ c}}{{\text{m}}^2}$. If the slant height of the cone is 8 cm, find the radius of the base.

Hint- Here, we will be using the formula Curved surface area of the cone = $\pi rl$ where it is already given with the curved surface area and the slant height of the cone. This will lead to the value of the radius of the base of the cone.
Given, Curved surface area of the cone = $60\pi {\text{ c}}{{\text{m}}^2}$
Curved surface area of the cone = $\pi rl$
$\Rightarrow 60\pi = \pi r\left( 8 \right) \Rightarrow \dfrac{{60}}{8} = r \Rightarrow r = \dfrac{{15}}{2} = 7.5{\text{ cm}}$
Note- In these types of problems, if instead of the slant height of the cone we are given with the height of the cone. Then, we will evaluate the slant height of the cone (in terms of radius of base of the cone r) using the formula $l = \sqrt {{h^2} + {r^2}}$ and then use the formula for curved surface area of the cone.