# Find the volume of the solid?

1. Feb 3, 2015

### Math10

1. The problem statement, all variables and given/known data
Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.

2. Relevant equations
None.

3. The attempt at a solution
This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?

2. Feb 3, 2015

### Staff: Mentor

Setting these integrals up is often the hardest part. Have you drawn a sketch of the solid?

3. Feb 3, 2015

### Ray Vickson

Please show you solution efforts. However, to help you start, here is a hint: when doing double or triple integral problems, always, always, always make a sketch of the integration region. It will help you figure out what your next steps should be.

4. Feb 3, 2015

### RUber

You can write z in terms of y and x in terms of y, so I would recommend y be your outer integral. Neither z nor x depend on eachother, so their order should not matter.

5. Feb 3, 2015

6. Feb 3, 2015

### LCKurtz

Neither of which is relevant to this problem.

7. Feb 3, 2015

### Svein

x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.

8. Feb 3, 2015

### LCKurtz

No, that is the three coordinate planes. He wrote what he meant there.

9. Feb 3, 2015

### Svein

Ah. Sorry.

10. Feb 3, 2015

### Staff: Mentor

Yes that's true but the real point of the post was to tell the OP about a resource that would help him which was located near these references.