Question

The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic metre, find the slant height and the radius (Use $\mathrm{\pi }=3.14$).

Answer 1

It is given that the ratio between the radius ‘r’ and the height ‘h’ of the cone is 5: 12.

Since only the ratio is given, to use them in an equation we introduce a constant ‘k’.

So,

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume =

The volume of the cone is given as

Substituting the values of and and using in the formula for the volume of a cone,

Volume =

314 =

= 1

k = 1

Therefore the actual value of the base radius is r = 5 m and h = 12 m.

Hence the radius of the cone is

We are given that r = 5 m and h = 12 m. We find l using the relation

=

=

=

= 13.

Therefore, the slant height of the given cone is

Hence the radius of cone and slant height is 5 m and 13 m respectively