Calculate Volume of Solid with Hole: Ball of Radius 12 and Hole of Radius 7

[ratroll01]

Homework Statement

A ball of radius 12 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.

Homework Equations

The Attempt at a Solution

I tried to do it as though it is a ball with a radius of 12 missing a ball with a radius of 7 from its center and got an answer around 2900. But it is actually a ball with a radius of 12 with a hole of radius of center, if that makes sense. Like you could see through the ball. I have no idea how to approach this..

 

[descendency]

Do you need an exact answer? You could approximate it very easily by using the volume of a sphere with 12 as it's radius and subtract the volume of a cylinder with radius 7 and height 12?

edit: The exact answer is obtained (one way) by using the equation for a circle (x*x + y*y = r*r, solve for the necessary variable) and the indefinite integral formula for finding volume (remember to choose the right limits).

First consider the case where the semi-circle is touching the Y axis. What is the radius of the hole generated by the volume created by revolution about the y axis?

picture:

http://img132.imageshack.us/img132/1650/helpbn7.jpg