Question

If the heights of two cones are in the ratio of 1 : 4 and the radii of their bases are in the ratio 4 : 1, then the ratio of their volumes is

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 1

Answer 1

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

Volume =

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

It is given that the ratio between the heights 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 radius of the two cones is 4 : 1.

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

So, = 4p

= 1p

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

=

=

Hence the correct choice is option (d).