(Q14).A cylinder and cone have bases of equal radii and are of equal heights. Show that their volumes are in the ratio of 3 : 1.

Given dimensions are:

Cone:

Radius = r

Height = h

Volume (V) =
1
3
 πr2h

Cylinder:

Radius = r

Height = h

Volume (V) = πr2h

Ratio of volumes of cylinder and cone = πr2h :
1
3
 πr2h
= :

= :

Hence, their volumes are in the ratio = : .