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

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