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)

Given: Volume of cone = 314 m³

Radius of base of cone: height of cone = r : h

= 5 : 12

Let radius of base of cone (r) = 5x

And let height of cone (h) = 12x

Volume of cone is given by,

Volume = πr²h/3

Substituting values, we get

314 = (3.14 × (5x)² × 12x)/3

⇒

⇒ x³ = 1

⇒ x = 1

Thus, radius of the base of cone = 5×1 = 5 m

And height of cone = 12×1 = 12 m

For slant height, we have the relation

l = √(r² + h²)

⇒ l = √(5² + 12²)

⇒ l = √(25 + 144)

⇒ l = √169

⇒ l = 13

Hence, we have got perpendicular height of cone to be 12 m and slant height of the cone to be 13 m.