# Solid of Revolution Problem

1. Dec 29, 2011

### Joe_K

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

Find the volume obtained by rotating the solid about the specified line.

y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.

2. Relevant equations

I used the disk method

3. The attempt at a solution

I drew a sketch and used disk method. For the radius I used 2-(1/2)x with a height of 1, and integrated. For an answer, I came up with 5pi/4. Does this seem correct? Thanks!

2. Dec 29, 2011

### tylerc1991

I am getting a different answer. What are your bounds? What is the integrand?

3. Dec 29, 2011

### Joe_K

My bounds were from 1 to 2.

4. Dec 29, 2011

### tylerc1991

That is correct. What about the integrand?

5. Dec 29, 2011

### SammyS

Staff Emeritus
What do you mean by "with a height of 1" ?

What function did you integrate?

6. Dec 29, 2011

### Joe_K

Sorry, I don't know why I typed height, I meant to say that that the bounds were 1 to 2. For the integrand I just had pi*2-(1/2)x*1 dx

7. Dec 29, 2011

### tylerc1991

The area of one of the disks is going to be $\pi \cdot (2 - \frac{1}{2} x)^2$. What happens when we sum those disks from $x = 1$ to $x = 2$?

8. Dec 29, 2011

### Joe_K

I think I forgot to square the radius when I originally did it. I redid the problem and came up with 19pi/12. Is this still wrong?

9. Dec 29, 2011

### tylerc1991

That is the answer I got.

10. Dec 29, 2011

### Joe_K

Awesome. Thanks guys!