Final answer:
To find the volume of the part of the ball that lies between φ=6π and φ=3π, use the formula for the volume of a spherical cap.
Step-by-step explanation:
The volume of the part of the ball that lies between φ=6π and φ=3π can be found by subtracting the volumes of two spherical caps. The formula for the volume of a spherical cap is 1/3 πh (3a²+h²), where a is the radius of the sphere and h is the height of the cap. In this case, a is the radius of the ball and h is the difference between the two angles, 6π and 3π. Substitute the values of a and h into the formula and evaluate to find the volume.