The radius of the base of a right circular cone is 7 cm and its curved surface area is 550 cm. The volume of the cone is:

Use $$\left(\pi = \frac{22}{7}\right)$$​​

Correct option is D

Given:
Radius of the base (r) = 7 cm
Curved Surface Area (CSA) = 550 cm²

Formula Used:
Curved Surface Area (CSA) of a cone = $$\pi rl$$​​

​Volume of a cone = $$\frac{1}{3} \pi r^2 h$$​​

Solution:

CSA of cone  = 550 cm²​

​$$\frac{22}{7} \times 7 \times l = 550\\ \ \\l = 25 \, \text{cm}\\ \ \\h = \sqrt{25^2 - 7^2} = 24 \, \text{cm}$$​​

Volume of the cone = $$\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 24 = 1232 \, \text{cm}^3$$​​