The radius and height of a right circular cone are in the ratio 3 : 4. If its curved surface area (in cm²) is 240π. Then its volume (in cm³) is:

Solution (By Examveda Team)

r : h = 3 : 4
$$l$$ : r = 5 : 3

$$\eqalign{ & {\text{Curved surface area}} = \pi rl \cr & 240\pi = \pi \times 3x \times 5x \cr & {x^2} = 16 \cr & x = 4 \cr & \therefore r = 3 \times 4 = 12 \cr & {\text{Volume}} = \frac{1}{3}\pi {r^2}h \cr & = \frac{1}{3}\pi \times 144 \times 16 \cr & = 768\pi \cr} $$