Question

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone.
(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 =

2512 =

= 8

k = 2

Therefore the actual value of the base radius is r = 10 cm and h = 24 cm.

Hence the radius of the cone is

We are given that r = 10 cm and h = 24 cm. We find l using the relation

=

=

=

= 26

Therefore the slant height of the given cone is

Hence the radius and slant height of the cone are 10 cm and 26 cm respectively