Question

The radius and the height of a rightr circular cone are in the ratio 5 : 12. If its volume is 314 cubic metre, find the slant height and the radius (Use π =3.14).

Answer 1

The slant height of the cone = 13 m

The radius of the cone = 5 m

Let the slant height of the cone be equal to l and the radius of the cone be r.

Given that the ratio of radius and the height (h) of the cone is 5/12 , r/h = 5/12

=> h = 12r/5

As we know in a cone , l² = h² + r²

=> l² = (12r/5)² + r²

=> l² = 169r²/25

=> l = 13r/5

Volume of the cone = 314 m³

=> 1/3 πr² h = 314

=> 1/3 × 3.14 × (12/5) × r³ = 314

=> r³ = 125

=> r = 5 m

slant height = l = 13r/5 = 13 m