A cylindrical drill with radius 5 inches is used to bore a hole through the center of a sphere of radius 7 inches. Find the exact volume of the ring-shaped solid that remains.

Answer 1

Let z=sqrt(49-x²-y²) .... find the volume removed by the drill bounded by the x-y, x-z and y-z planes and muliply by 8, then subtract that from 49*4/3pi for the final answer.

The volume removed by the drill = 8* (double integral of zdxdy ) the x limits are 0 to sqrt(25-y²) and the y limits are 0 to 5. I got 952pi/3.