A ball of radius 11 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Find it using integrals.

Expert Answers

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The ball is a sphere.

Volume of a sphere:  4/3 * `pi` * r^3

The radius of the ball is 11.

4/3 * `pi` * 11^3 = 5324/3 * `pi`

The volume of the ball is 5324/3 * ``

The hole drilled through the ball is a cylinder.

Volume of a cylinder:  `pi` * r^2 * h

The radius of the hole is 5.  The height of the cylinder is the same as the diameter of the ball, so the height is 22. 

`pi` * 5^2 * 22 = 550 * `pi`

To find the volume of the resulting solid, subtract the volume of the cylinder from the volume of the sphere.

(5324/3 * `pi` ) - (550 * `pi` ) = 3674/3 `pi`

`~~` 1224.67`pi`

`~~` 3847.4

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