Question

The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3, Find the ratio of their vertical heights.

Answer 1

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

Volume =

Let the volume, base radius and the height of the two cones be and respectively.

It is given that the ratio between the volumes of the two cones is 4: 5.

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

So, = 4k

= 5k

It is also given that the ratio between the base radiuses of the two cones is 2: 3.

Again, since only the ratio is given, to use them in our equation we introduce another constant ‘p’.

So, = 2p

= 3p

Substituting these values in the formula for volume of cone we get,

=

=

=

=

Therefore the ratio between the heights of the two cones is