Question

sphere is cut into 8 congruent pieces. The radius of the sphere is 8 centimeters. One piece is shown in the diagram.



What is the surface area of one piece of the sphere, as shown in the diagram? Express the answer in terms of π.

64π cm2
80π cm2
256π cm2
384π cm2

Answer 1

Total sphere area = 4πr^2 = 4π(8^2) = 256π. Each congruent piece gets 1/8 of the spherical surface: (1/8)·256π = 32π.

Each of the three plane faces on the piece is a quarter-disk of radius 8, area (1/4)π(8^2) = 16π. Three such faces contribute 3·16π = 48π.

Total surface area of one piece = 32π + 48π = 80π cm^2.

Answer: 80π cm^2.