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!
$\endgroup$ 21 Answer
$\begingroup$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 $$ V = \frac{\pi h^2}{3}(3r - h) $$
$\endgroup$
