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Also this is the top half calculation and I would take the final answer times 2.

P.S. I will try and post my handwritten notes of my rework.

drilled sphere i mean. sigh

Ok, yes, I got the same equation as you :D. I had to solve this one tonight. I double checked my answer by also finding the drilled portion and adding it to my answer which gave a total volume exactly equal to the volume of a sphere of the same radius. I have posted my final notes for anyone else wanting to see the solution (after they attempted of course :D).
P.S. I appreciate the dialog Xavier as it has been helping me when I get stuck!

Glad to help. Also a u substitution with u=a^2-x^2 would have made it a bit less work.

Heh, yeah, I have been doing too many trig subs lately.