Spherical Section Volume

[Moose352]

How do I find the volume of a bowl shaped section of a sphere, given the depth of the section. I know i can integrate it, but a friend says that i can find the volume of a cone with equal height and radius, and then use that to find the volume of the spherical section.

[Tide]

Find the volume of the sector of the sphere that includes the bowl and subtract from it that volume of a cone whose vertex is at the center of the cone and whose base is the (flat) top of the bowl.

[Moose352]

Thanks Tide, but the equation for the sector of a sphere is derived using calculus. Is there any way to find the equation for the spherical cap without calculus? And by calculus, i mean integration.

[Tide]

I don't know if there is a way to do it without calculus but I think the point is that it is a lot easier to find the desired volume using the sector and cone approach than it is to integrate directly. If someone is clever enough to get it without calculus I'd love to see it!