# Find the volume of the solid?

## Homework Statement

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.

None.

## 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?

Mark44
Mentor

## Homework Statement

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.

None.

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

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

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.

None.

## 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?

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.

RUber
Homework Helper
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.

LCKurtz
Homework Helper
Gold Member
You need to setup the integral and then you'll know how to setup the limits.

There are some videos on the mathispower4u that talk about the washer method and the shell method:
Neither of which is relevant to this problem.

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

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

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

Svein