SOLUTION: A 4-in auger hole is bored through a 10-in sphere, the axis of the hole coinciding with a diameter of the sphere. Find the volume bored out.

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Question 1181642: A 4-in auger hole is bored through a 10-in sphere, the axis of the hole coinciding with a diameter of the sphere. Find the volume bored out.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the numbers refer to the diameters of the sphere and hole
One interesting fact about spheres with holes bored through the diameter is:
The volume that remains is equal to the volume of a sphere with the diameter
equal to the height of the hole
The volume that remains after the hole is drilled is 4/3pi*h^3 where h is
the half-height of the hole. The radius of the sphere, the radius of the hole
and h form a right triangle. Thus h = sqrt(5^2-2^2)
So the bored out volume = 4/3pi*5^3 - 4/3pi*h^3 = 523.6 - 403.1 = 120.5 in^3