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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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