Question:
The radius and slant height of a cone are in the ratio 4: 7.If its curved surface area is $792 \mathrm{~cm}^{2}$, find its radius.
Solution:
It is given that
Curved surface area = πrl = 792
Let the radius (r) = 4x
Height (h) = 7x
Now,
C. S. A = 792
22/7 ∗ 4x ∗ 7x = 792
$\Rightarrow 88 x^{2}=792$
$\Rightarrow x^{2}=792 / 88=9$
⟹ x = 3
Therefore Radius = 4x = 4 * 3 = 12 cm