jmc

Question

A sphere is cut into four congruent wedges. The circumference of the sphere is

12 π

inches. What is the number of cubic inches in the volume of one wedge? Express your answer in terms of

π

.

Note: To measure the circumference, take the largest circle on the surface of the sphere.

Accepted Answer

Let the sphere's radius be r. From the sphere's circumference we have 2 r = 12; solving for r yields r = 6. The volume of the sphere is 43 r^3 = 43 (6^3) = 36 8 . The volume of one wedge is one-fourth this volume, or 14 6^2 8 = 6^2 2 = 72.