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.
So first we need to find the radius of the sphere. The circumference of the sphere is $12\pi$ inches. We know that the circumference of a circle is $2\pi r$, where r is the radius. So the radius of the sphere is 6 inches. The volume of the whole sphere is $\frac{4}{3}\pi r^3$, which is $\frac{4}{3}\pi 6^3$, which is $\frac{4}{3}\pi 216$, which is $288\pi$. So the volume of one of the four congruent wedges is $\frac{1}{4} \cdot 288\pi$, which is $72\pi$.

