Question

The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes. 

Answer 1

Let radius of first cone be 3r and height be h, then radius of second cone will be rand height will be 3h. 

Volume of cone = `1/3 xx (pir^2) xx h`

Ratio of volumes of cone = `"Volume of first cone"/"Volume of second cone"`

= `(1/3 xx (pi(3r)^2) xx h)/(1/3 xx (pir^2) xx 3h)`

= `(1/3 pi9r^2h)/(1/3pir^2 3h)`

= `3/1`

Ratio of volumes of cone = 3:1