Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice
perpendicularly to the cylinder's
axis. Then the lateral surface area of the spherical
segment
is equal to the lateral surface area cut out of the
cylinder
by the same slicing planes, i.e.,
where
is the radius of the cylinder
(and tangent sphere) and
is the height of the cylindrical (and spherical) segment.