The radius and height of a right circular cone are in the ratio 5 : 12. If its curved surface area is 816.4 cm², then volume of this cone is (taking \(\pi \) = 3.14):

2,512 cm³

If r = 5x, h = 12x

⇒ l = \(\sqrt {r^2 + h^2}\) = \(\sqrt {(5x)^2 +(12x)^2}\) = 13 x

⇒ C.S.A. = \(\pi \)rl

⇒ 816.4 = 3.14 × 5x × 13 x

⇒ x² = 4                                

⇒ x = 2 cm

⇒  So, r = 10 cm and h= 24 cm

Volume = \(\frac{1}{3}\)\(\pi \)r²h

            = \(\frac{1}{3}\) × 3.14 × 100 × 24 = 2,512 cm³