# Volume of a torus

1. Mar 21, 2009

### KevinL

1. The problem statement, all variables and given/known data
http://faculty.tcu.edu/richardson/Calc2/H20090323torusVolume.htm [Broken] This is a link to the homework.

2. The attempt at a solution
I did number 1 by doing 2 * integral from -2 to 2 of sqrt(4-x^2) = 4pi

The second problem is where im completely confused and dont know how to do it or even conceptualize it. Trying to look at an example of a similar problem on another site, I tried to do 4pi * integral from -2 to 2 of xsqrt(4-x^2) but it equals 0.

I think if I understand this one ill be able to do the rest of the homework.

Last edited by a moderator: May 4, 2017
2. Mar 21, 2009

### Dick

You are close. But the x in the second integral is supposed to be the radius of rotation of the slice located at x and rotated around x=3. How far is x from the center of rotation at x=3?

3. Mar 21, 2009

### KevinL

So it should be 4pi * integral from -2 to 2 of 3sqrt(4-x^2) ?

4. Mar 21, 2009

### Dick

No. If x is -2 the radius of rotation is 5. If x is +2 the radius of rotation is 1. Right? The distance of those points from x=3. What is the radius for a general point x between -2 and 2?

5. Mar 21, 2009

### KevinL

r= 3-x

6. Mar 21, 2009