If the curved surface area of a right circular cone is 10010 sq cm and its radius is 35 cm, find its volume?

Let slant height of cone = $$l$$ cm and radius = 35 cm

Curved surface area of cone = $$\pi r l = 10010$$

=> $$\frac{22}{7} \times 35 \times l = 10010$$

=> $$22 \times 5 \times l = 10010$$

=> $$l = \frac{10010}{110} = 91$$

Let height of cone = $$h$$ cm

=> $$(h)^2 = (l)^2 - (r)^2$$

=> $$(h)^2 = (91)^2 - (35)^2$$

=> $$(h)^2 = 8281 - 1225 = 7056$$

=> $$h = \sqrt{7056} = 84$$

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

= $$\frac{1}{3} \times \frac{22}{7} \times (35)^2 \times 84$$

= $$22 \times (35)^2 \times 4 = 107800 cm^3$$