How do I find the volume of a sphere drilled into by a cylinder?

Fench

New member
I have a homework problem: A cylindrical drill with radius 5 is used to bore a hole through the center of a sphere of radius 7. Find the volume of the ring shaped solid that remains.

I know this involves double integrals, but I have no idea how to go about implementing it. Any help would be appreciated, thank you.
 
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