Find the volume of the solid?

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  • #1
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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.

Homework Equations


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?
 

Answers and Replies

  • #2
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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.

Homework Equations


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?
 
  • #3
Ray Vickson
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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.

Homework Equations


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.
 
  • #4
RUber
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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.
 
  • #6
LCKurtz
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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.
 
  • #7
Svein
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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.
 
  • #8
LCKurtz
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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.
 
  • #10
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Neither of which is relevant to this problem.
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.
 

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