The radii of a right circular cone and a right circular cylinder are in the ratio 2 : 3. If the ratio of the heights of the cone and the cylinder is 3 : 4, then what is the ratio of the volumes of the cone and the cylinder?

1 : 9

We know that,

Volume of Cone = $\frac{1}{3}$πr²h

Volume of Cylinder = πr²h

Ratio of radius of right circular cone to right circular cylinder = 2:3

Ratio of height of the right circular cone to right circular cylinder = 3:4

Now according to the formula =

The ratio of the volumes of both of them =

$\frac{1}{3}$πr²h :  πr²h

$\frac{1}{3}$(2)²3 :  (3)²4

4 :  36 = 1 : 9