Large bowl and small bowl ratio of liquid

Question

A large bowl has a radius R and height H

A small bowl has a radius 5/6 R and a height 2/3 H

What is the ratio of liquid in the bowls?

I'm stumped on how to do this one

Answer 1

The volume of a bowl is going to be directly proportional to the product of its height and the square of its radius. $$V=kR^2H$$

Replacing $R$ with $\frac{5R}{6}$ and $H$ with $\frac{2H}{3}$ gives a volume of $$V=k(\frac{5R}{6})^2\frac{2H}{3}=\frac{25}{54}kR^2H$$

Therefore, the ratio of the volume of the large bowl to the small bowl is $\frac{54}{25}$.