Is My Integral Calculation Correct for Finding the Volume of a Drilled Sphere?

[blumfeld0]

so i have one problem and i just need to know if my integral is right. any help would be greatly appreciated

1. a ball of radius 10 has a round hole of radius 5 drilled through its center. find the volume of the resulting solid.

i know volume of cylinder removed is pi*5^2*10*sqrt(3)

because h^2/4 + 5^2=10^2 so h = sqrt(300)= 10*sqrt(3)

and i know the volume of original sphere is 4/3*pi*10^3

and now what?
i think i need to do integral of pi*(100-y^2) dy from 10 to 10*sqrt(3) and multiply this whole answer by 2
is that right?

if so what do i do with these three pieces of information? thank you!

 

[arildno]

I advise you to be meticulous in setting up the limits of integration.