Volume of Solid Between Curves: Region, Sketch, and Solution

In summary: In this case, since the problem does not specify, either orientation is possible. However, the sketch should show the orientation and the solution should specify which orientation is used.In summary, the task at hand is to find the volume of a solid obtained by rotating a region bounded by given curves around a specified line. A sketch of the region, solid, and a typical disk or washer should also be provided. When working on the problem, it is important to correctly identify the line of rotation and the orientation of the disks or washers. Additionally, submitting one problem at a time may yield better results in receiving help. In problem #4, the last three equations (y = 0, x = 2, x = 4) are
  • #1
phillyolly
157
0

Homework Statement



Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

Homework Equations





The Attempt at a Solution



Sometimes, I struggled with drawing a solid and a typical disc. Also, I am unsure with the solution for problem 4. Do you see any mistakes?

I would so much appreciate your help.
 

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  • #2
This is a rare time when no one replied. Sad.
 
  • #3
You'll probably do better submitting one problem at a time.

The first couple of problems are missing some information - namely, the line around which the region is rotated. For example, in #2, you have the region bounded by y = 1 - x2 and y = 0, but you didn't say what this region is rotated around.
 
  • #4
It's probably rotated around y = 0, especially since the problem mentions "disk and washer."

I'm guessing the cylinder shape you drew was supposed to be a typical disk/washer the problem asked for, but that's not what you want. When the region is rotated around a horizontal line, disks and washers will be vertical, between the axis of revolution and the function for disks or between the two given functions for washers.

On #4, what are the last three equations for?
y = 0, x = 2, x = 4
 
  • #5
Bohrok said:
It's probably rotated around y = 0, especially since the problem mentions "disk and washer."
Disks and washers can be oriented either vertically or horizontally.
 

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