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:

Answer: Option D

Solution

Answer: Option D

Solution:

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

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