### Instruction: A sphere is cut into four congruent wedges. The circumference of the sphere is $12\pi$ inches. What is the number of cubic inches in the volume of one wedge? Express your answer in terms of $\pi$.

Note: To measure the circumference, take the largest circle on the surface of the sphere.### Response: So the circumference of the sphere is $12\pi$ inches. So the radius of the sphere is $6$ inches because $12\pi = 2\pi r$ and $r = 6$.
So the radius of the sphere is 6. One fourth of the volume of the sphere is one of the wedges.
The volume of the sphere is $\frac{4}{3}\pi r^3 = \frac{4}{3}\pi 6^3 = \frac{4}{3}\pi 216 = 288\pi$
So one fourth of the volume of the sphere is $72\pi$.