Volume by Cylindrical Shells (need verification)

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A hole of radius [tex]\sqrt{3}[/tex] is bored through the center of a sphere of radius 2. Find the volume removed


4[tex]\pi[/tex][tex]\int[/tex][tex]\intx\sqrt{a^{2}-x^{2}}dx[/tex] from [tex]\sqrt{3}[/tex] to 2[tex]\sqrt{3}[/tex]?

And then subtract this from the volume of the sphere?
 
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or is it from route of 3 to 2?
 

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