Express the volume as a function of the height

Question

A conical cup is 9 inches high and its radius across the top is 2 inches. If the cup contains liquid, express the volume of the liquid as a function of the height of the liquid.

Answer 1

Volume= $\pi \ \ r^{2} h/3$

So in your case, $ V= \pi \ (r^{2}) h/3$

$f(h) = 4 ( \pi) h/3$

Answer 2

Hint: if two solids are similar and their similarity ratio is $a$, then their volumes are in the ratio of $a^3$.