Question

Consider a sphere container with radius R.

1. Suppose it is filled to height h, below halfway, with water. Find the volume of the water.

2. What is the proportion of the sphere's total volume taken up by the water filled as described in problem #1?

3. Suppose it us filled to height,H, above halfway with water. Find the volume of the water.

4. Give a formula for the volume of water filled to arbitrary height h, regardless of it being above or below the halfway mark, as a function V(h).

Answer 1

the spherical cap is discussed below. Having the answer to part (4) make sthe other parts easy.

http://mathworld.wolfram.com/SphericalCap.html