The heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4. Find the ratio of their volumes?

The volume of a cone can be written as $$\pi r^2h$$. 
Where r is the radius of the base of the cone and h is the height of the cone.

The heights of two right circular cones are in the ratio 1 : 2, 
Let us say, H1 is 1X and H2 is 2X

Perimeters of their bases are in the ratio 3 : 4, 
Let us say, $$\2pi r_1$$ is 3Y and $$\2pi r_1$$ is 4Y. 

$$r1=\frac{3Y}{2\pi\ }$$ and $$r2=\frac{4Y}{2\pi\ }$$

Volume of cone 1 will be, $$\pi\left(\frac{3Y}{2\pi\ }\right)^2\left(X\right)$$

Volume of cone 2 will be, $$\pi\left(\frac{4Y}{2\pi\ }\right)^2\left(2X\right)$$

The ratio will hence be 9:32.