Chapter 8.2, Problem 36E

(a) Show that the surface area of a zone of a sphere that lies between two parallel planes is S = 2πRh, where R is the radius of the sphere and h is the distance between the planes. (Notice that S depends only on the distance between the planes and not on their location, provided that both planes intersect the sphere.)

(b) Show that the surface area of a zone of a cylinder with radius R and height h is the same as the surface area of the zone of a sphere in part (a).