Finding the maximum volume of a cone

Question

21. You have a 6 inch diameter circle of paper which you want to form into a drinking cup by removing a pie–shaped wedge and forming the remaining paper into a cone (Fig. 22). Find the height and top radius of so the volume of the cup is as large as possible.

This is a question from Saylor Academy.
I am working on this problem, and I can understand that the volume is $1/3 \pi r^2 h$. But, I cannot understand how to figure out what h is. The answer key gives it as the $\sqrt{9-r^{2}}$. Why?

Answer 1

Does this side view of your cone help?

I answered your question "why."

Answer 2

$V=\frac 13\pi r^2h$. But by the Pythagorean theorem, $h^2+r^2=3^2$.