The radius and slant height of a cone are in the ratio of $4 : 7$. If its curved surface area is $792\ cm^2$, find its radius.

 Given:

The radius and slant height of a cone are in the ratio of $4 : 7$.

Its curved surface area is $792\ cm^2$.

To do:

We have to find its radius.

Solution:

Curved surface area of the cone $= 792\ cm^2$

Ratio of the radius and slant height $= 4:7$

Let the radius be $4x$ and the slant height be $7x$.

Therefore,

$\pi rl = 792$

$\frac{22}{7} \times 4 x \times 7 x=792$

$88 x^{2}=792$

$x^{2}=\frac{792}{88}$

$x^2=9$

$\Rightarrow x=\sqrt{9}$

$x=3$

This implies,

Radius $=4 x$

$=4 \times 3$

$=12 \mathrm{~cm}$

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Updated on: 10-Oct-2022

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