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?

Volume of right circular cone = $$\frac{1}{3} $$ $$\pi\times{ r_{1}^2 h_{1}}$$

Volume of right circular cylinder =  $$\pi \times{ r_{2}^2 h_{2}}$$

,where $$ r_{1}$$,$$h_{1}$$ and $$ r_{2}$$,$$h_{2}$$ is radius and height of cone and cylinder respectively.

The given ratio of radius of cone to cylinder =$$\frac{2}{3} $$

The given ratio of heights of cone to cylinder = $$\frac{3}{4}$$

Putting this in the formula we get the ratio of right circular cone to right circular cylinder =$$\frac{(\frac{1}{3} \pi\times{ r_{1}^2 h_{1}})}{(\pi \times{ r_{2}^2 h_{2}})}$$

= $$\frac{(\frac{1}{3}\pi\times2^2\times\ 3)}{(\pi\times3^2\times\ 4)}$$

After solving we get $$\frac{4}{36}$$
Hence,the ratio of area of right circular cone to right circular cylinder is = $$\frac{1}{9}$$