Question

If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height. (π = 3.14)

Answer 1

The ratio of radius of base and perpendicular height of a cone is 5 : 12.

Let the radius of base and perpendicular height of the cone be 5x and 12x, respectively.

Volume of the cone = 314 m³

∴ `1/3`πr²h = 314 m³

⇒ `1/3 xx 3.14 xx (5x)^2 xx 12x` = 314

⇒ 314 x³ = 314

⇒ x³ = 1

⇒ x = 1

∴ Perpendicular height of the cone = 12x = 12 × 1 = 12 m

Radius of the cone = 5x = 5 × 1 = 5 m

Now,

l² = r² + h²

⇒ l² = (12)² + (5)²

⇒ l² = 144 + 25

⇒ l² = 169

⇒ l² = (13)²

⇒ l = 13 m

Thus, the perpendicular height and slant height of the cone is 12 m and 13 m, respectively.