calculus
posted by Ruby .
A ball of radius 10 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.

whole ball = 4/3(pi)(10^3)= (4000/3)(pi)
now drill out the integral of Pi(y^2)dx from 4 to 4 or
2pi(integral)(100x^2)dx from 0 to 4
= 2pi [ 100x  (1/3)x^3] from 0 to 4
= 2pi(400  64/3]
= 2pi(1136/3)
so the volume of the solid is
4000pi/3  2275pi/3 = 1728pi/3
please check my arithmetic.
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