Problem with finding volume using shells

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In summary, the conversation discusses the process of finding the volume of a solid generated by revolving a region bounded by two curves around the y-axis. The volume is found using an integral and the radius of the hole can be determined by setting the integral equal to the desired volume and solving for the radius.
  • #1
asadpasat
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A solid is generated by revolving the region bounded by y=(1/2)x2 and y= 2 about the y-axis.
So what I did is set up my integral V= 2pi (integral sign from 0 to 2) x(1/2)(x)2 dx
When I solve i get 4pi, and then I have to find the radius of the hole which has one fourth of the volume. So the volume of the hole is pi ( the hole is centered around the axis of revolution which is y-axis). Then I set equal integral from 0 to r (the radius of the hole ) is 2pi(1/2)(x3)dx = pi. the answer i get is 41/2, which is not right as i checked
 
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  • #2
This appears to be a homework problem or one in a textbook. @asadpasat, please start a new thread in the Homework and Coursework section (Calculus subsection). This forum section is for conceptual calculus questions, not for homework problems.
Thanks...
 
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Related to Problem with finding volume using shells

1. What are shells and how are they used to find volume?

Shells are a geometric concept used in calculus to find the volume of three-dimensional shapes. They involve taking a thin "shell" or layer of a shape and integrating it to find the total volume.

2. What is the problem with using shells to find volume?

The main problem with using shells to find volume is that it can be difficult to determine the correct integration limits, leading to incorrect results. This is especially true for more complex shapes.

3. How can I avoid errors when using shells to find volume?

To avoid errors, it is important to carefully visualize the shape and determine the correct integration limits before attempting to use shells to find volume. It may also be helpful to break the shape into smaller, more manageable parts.

4. Are there any other methods for finding volume besides using shells?

Yes, there are other methods for finding volume, such as using disks or washers. These methods may be more suitable for certain shapes and can help avoid the potential errors associated with using shells.

5. Can shells be used to find the volume of any shape?

No, shells are only applicable to certain shapes, such as solids of revolution. Other shapes may require different integration techniques or may not be able to be solved using calculus methods at all.

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