Question

If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is

(a) 1 : 5

(b) 5 : 4

(c) 5 : 16

(d) 25 : 64

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 1 : 4.

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

So, = 1k

= 4k

It is also given that the ratio between the base diameters of the two cones is 4 : 5.

Hence the ratio between the base radius will also be 4 : 5.

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

So, = 4p

= 5p

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

=

=

=

=

Hence the correct answer is option (d).