I'm not sure if this isn't part of Calculus but it's in my Calculus text book so sorry if I am posting in the wrong place.

How do I calculate the volume of the cap (=top) of a sphere such as the part indicated in blue of my drawing where the black colour refers to the rest of the sphere? I don't even know how to get started. All I know is the volume of the whole sphere is 4/3 * pi*r^3 and I'm thinking that the 4/3 needs to be 4/6 = 2/3 or something after because it's like a "mini-semisphere."

The question as written from the text book is:

"Find the volume of the described solid S; A cap of a sphere with radius r and height h."

The answer is:

V = pi * h^2 * (r - 1/3 * h)

Any help would be greatly appreciated!

Thanks in advance!