Volume bounded by cylinder and planes

In summary: Post the image so that we can see what you're working with.The problem is stated very succinctly in the textbook as post 1 without more or without fewer words.
  • #1
ostrogradsky
8
0
Must double integrate using type I or type II planar region D to find volume bounded by

Cylinder y^2+z^2=4

And

Planes
X=2y
X=0
Z=0

ImageUploadedByPhysics Forums1409498322.749856.jpg
ImageUploadedByPhysics Forums1409498356.193466.jpg
 
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  • #2
Many of the regulars here, myself included, will not help on question that is posted as an image, let alone sideways, instead of typing it as forum guidelines specify. Read vela's guidelines for posting at the top of this forum.
 
  • #3
The two pictures include my attempt at the answer.
 
  • #4
What else would you like? The problem is stated very succinctly in the textbook as post 1 without more or without fewer words.

The pictures are my attempts at deriving the answer to this NOT simple problem.
 
  • #5
I wish to double check my answer and see if there are additional ways without using polar coordinates to get to the answer.
 
  • #6
I agree with LCKurtz. If you want help with your problem, at least put in the effort to post the (second) image so that one can read it without too much effort. Besides being sideways, it appears that your photo cuts off some of your work at the boundaries of the image.

Better yet, post the work directly in the text window.
 
  • #7
This problem requires a picture in order to solve it.

I provided the essential picture, yet I am getting complaints about posting a picture.

I am assuming that you all did not even attempt to think about this problem.
 
  • #8
So you are paying NO attention to what you were told?
 
  • #9
Double integral (4-y^2)^.5 dy dx from x=0 to 4 and y=-2 to x/2
 
  • #10
You're going to have to look at picture to even make sense of the scribbles I wrote above. So no more complaints.
 
  • #11
ostrogradsky said:
You're going to have to look at picture to even make sense of the scribbles I wrote above. So no more complaints.
You have totally ignored the comments about this image being sideways.

attachment.php?attachmentid=72596&d=1409498356.jpg


It has also been pointed out that some information is cut off this image.The good folks who provide help on thts forum are volunteers.

Please try to work with us.
 
  • #12
ImageUploadedByPhysics Forums1409597372.145285.jpg


Done.
 
  • #13
ostrogradsky said:

Not done. There are still parts cut off at the edges.
By all means post the diagram as an image, but take the trouble to type all the equations in, preferably using LaTeX. It costs you maybe 10 minutes, but saves everyone else a few minutes each.
You want help, make it easy for people wishing to give you help.
 

1. What is the formula for finding the volume bounded by a cylinder and planes?

The formula for finding the volume of a shape bounded by a cylinder and planes is V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder.

2. How do you calculate the volume when the shape is bounded by multiple planes?

To calculate the volume when the shape is bounded by multiple planes, we need to find the volume of each individual shape and then subtract the overlapping areas. For example, if a cylinder is bounded by two planes, we would find the volume of the cylinder and then subtract the volume of the overlapping section.

3. Can the volume bounded by a cylinder and planes be negative?

No, the volume bounded by a cylinder and planes cannot be negative. It is a measure of physical space and therefore cannot have a negative value.

4. How do the positions and orientations of the planes affect the volume bounded by a cylinder?

The positions and orientations of the planes can greatly affect the volume bounded by a cylinder. If the planes are parallel to the base of the cylinder, the volume will be the same as the volume of a cylinder. However, if the planes are at an angle or intersect the cylinder, the volume will be different and will need to be calculated using the formula for finding the volume of a shape bounded by multiple planes.

5. Can the volume bounded by a cylinder and planes be greater than the volume of the cylinder itself?

Yes, it is possible for the volume bounded by a cylinder and planes to be greater than the volume of the cylinder itself. This can happen if the planes intersect the cylinder in a way that creates additional space within the boundaries of the shape.

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