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

Answer 1

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)(100-x^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.