The curved surface area of a right circular cone is 156 $\pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm$^3$?

240 $\pi$

We know that,

Curved surface area of cone = πrl

Vomume of cone = \(\frac{1}{3}\)πr²h

L² = r² + h²

Radius of cone = r = 12 cm

Curved surface area of cone =  πrl = 156π

= 12 × l = 156

l = 13

So, put the value of l and r in = l² = r² + h²

= 13² = 12² + h²

= h² = 169 – 144 = 25

=  h²  = 25

= h = 5 cm

Volume of cone =\(\frac{1}{3}\) × π × 12 × 12 × 5 = 240π