# Volume enclosed by a cone and a plane

1. Apr 20, 2014

### thonwer

1. The problem statement, all variables and given/known data
Find the volume enclosed by the cone x$^{2}$+y$^{2}$=z$^{2}$
and the plane 2z-y-2=0.

2. Relevant equations
$\int\int\int$ dV

3. The attempt at a solution
In the image Cono=Cone and Plano=Plane

2. Apr 20, 2014

### Staff: Mentor

Problems about integration should be posted in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.

3. Apr 21, 2014

### thonwer

I have tried to solve it in a different way but I do not think it is much better. Can anybody help me?

4. Apr 21, 2014

### LCKurtz

For what it's worth, I don't see anything obviously wrong with your work. I entered the $r,\theta$ integral you get into Maple and it just hung trying to solve it. I doubt you are going to find an elementary solution.

5. Apr 21, 2014

### thonwer

So my first attempt is OK? Because I'm finding troubles with the absolute value of (y) and (-y). I'm not sure if everything I've put is correct.

6. Apr 21, 2014

### LCKurtz

I didn't check your rectangular coordinate version. The $r,\theta$ change of variables you used would be the natural way to set it up and that's all I looked at.

7. Apr 21, 2014

### thonwer

If you do not mind could you please take a look at my rectangular coordinate version?