Finding the volume of a region

Question

Find the volume of the region inside the sphere x²+y²+z²=1 and outside the cylinder x²+y²=1/4. How would I set this up using the a triple integral?

Answer 1

If you visualize the cylinder inside the sphere and "piercing" thru the top and bottom of the sphere then if you take the full volume of the sphere and subtract the "normal" cylinder with flat circular top and bottom (no calculus so far) then the only thing left to subtract is the top (and equal) bottom pieces between the "top" of the flat cylinder and below the sphere.

 

see: https://www.wyzant.com/resources/files/451356/cylinder_in_sphere

 

I didn't do any calculus yet but do you understand what I have suggested?