If a sphere of radius is sliced by a plane whose distance from the center of the sphere is d, then the sphere is divided into two pieces called segments of one base. The corresponding surfaces are called spherical zones of one base.
(a) Determine the surface areas of the two spherical zones indicated in the figure.
(b) Determine the approximate area of the Arctic Ocean by assuming that it is approximately circular in shape, with center at the North Pole and €œcircumference€ at 75north latitude. Use r = 3960 mi for the radius of Earth.
(c) A sphere of radius is inscribed in a right circular cylinder of radius r, two planes perpendicular to the central axis of the cylinder and a distance apart cut off a spherical zone of two bases on the sphere. Show that the surface area of the spherical zone equals the surface area of the region that the two planes cut off on the cylinder.
(d) The Torrid Zone is the region on the surface of Earth that is between the Tropic of Cancer (23.45o north latitude) and the Tropic of Capricorn (23.45o south latitude) What is the area of the Torrid Zone?