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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.

Last updated date: 22nd Jul 2024
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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.

Complete step by step solution:
Let r be the radius of the base of the cone.
Given, Curved surface area of the cone = $60\pi {\text{ c}}{{\text{m}}^2}$
Also given, Slant height of the cone l = 8 cm
As we know that the formula for the curved surface area of the cone with radius of the base as r and slant height as l is given by
Curved surface area of the cone = $\pi rl$
$\Rightarrow 60\pi = \pi r\left( 8 \right) \Rightarrow \dfrac{{60}}{8} = r \Rightarrow r = \dfrac{{15}}{2} = 7.5{\text{ cm}}$
Therefore, the radius of the base of the given cone is 7.5 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.