Calculating the volume of a hemisphere given only the height

Question

So I have a math problem that I'm trying to solve with regards to hemispheres but am just confused about this part of the question

If I have a hemisphere with radius $r$, then

Volume $= \frac23\pi r^3$

However, how can I find some volume within the hemisphere if I am given the height only?

I've only used height of a hemisphere when I know it is equal to the radius but never less.

Thank you!

A hemisphere is half of a sphere, which is not what you want, I think. — bubba, Feb 21 '16 at 08:35

score 2 · Answer 1 · answered Feb 21 '16 at 08:34

2

It sounds like you're talking about a spherical cap.

If so, the volume of a spherical cap with height $h$ on a sphere with radius $r$ is $$ V = \frac{\pi h^2}{3}(3r - h) $$

answered Feb 21 '16 at 08:34

bubba

1 Answers1