A "spherical cap" is the volume of a sphere cut off by a plane. The volume can be expressed in terms of the radius (r) of the sphere and the (short) distance (h) from the plane to the sphere.

Volume = πh^2(r-h/3)

Obviously, if the depth is more than the radius (greater than half full), one can compute the empty volume from this formula and subtract that from the volume of the sphere.

Volume = πh^2(r-h/3)

Obviously, if the depth is more than the radius (greater than half full), one can compute the empty volume from this formula and subtract that from the volume of the sphere.