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

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SUMMARY

The discussion centers on calculating the volume of a solid formed by a sphere of radius 10 with a cylindrical hole of radius 5 drilled through its center. The volume of the cylinder removed is correctly identified as π * 5² * 10 * √3. The original sphere's volume is calculated as 4/3 * π * 10³. The user proposes using the integral of π * (100 - y²) dy from 10 to 10√3, multiplied by 2, to find the remaining volume, which is a valid approach for this problem.

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blumfeld0
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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!
 
Last edited:
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I advise you to be meticulous in setting up the limits of integration.
 

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