# Trickey volume question

1. Feb 4, 2009

### ratroll01

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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..

2. Feb 4, 2009

### 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:

Last edited: Feb 4, 2009