Finding Shell Radius: Why (3)^1/2 - (3-y^2)^1/2?

In summary, the formula for finding shell radius is (3)^1/2 - (3-y^2)^1/2. This formula is derived from the Pythagorean theorem and is commonly used in scientific research, particularly in fields related to physics and engineering. It can be rewritten as (3-y^2)^1/2 - (3)^1/2 and has some limitations, as it assumes a perfect shape and may not be accurate for extreme sizes.
  • #1
elfinitty
3
0

Homework Statement


30b1j4i.jpg

This is the main question.So I'm stuck at the b part
2nqcjfp.jpg

It says that the shell radius is (3)^1/2 - (3-y^2)^1/2 but i would only say (3-y^2)^1/2.Why do we say otherwise?

Homework Equations

The Attempt at a Solution


i would say the shell radius is (3-y^2)^1/2 but it's wrong
 
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  • #2
On my device at least your post is sideways so practically unreadable. I probably have nothing helpful to say on the problem, but possibly helpful is to tell you that people who could help won't if they can't read your post, and if it is difficult in such a careless way can be irritated and not want to take any trouble themselves.
 
  • #3
elfinitty said:

Homework Statement


[ IMG]http://i62.tinypic.com/30b1j4i.jpg[/PLAIN]
This is the main question.So I'm stuck at the b part
[ IMG]http://i61.tinypic.com/2nqcjfp.jpg[/PLAIN]
It says that the shell radius is (3)^1/2 - (3-y^2)^1/2 but i would only say (3-y^2)^1/2.Why do we say otherwise?

Homework Equations



The Attempt at a Solution


i would say the shell radius is (3-y^2)^1/2 but it's wrong
It was rather difficult to read. Moreover, it would have been helpful for you to have accompanied the images with more text explaining what you were trying to do here.

For using the shell method and revolving about the x-axis:
I would say the radius of the shell is y, the width is ##\displaystyle \ \sqrt{3}-\sqrt{3-y^2} \ ##, and the thickness is dy .
 
  • #4
Thread closed as posting homework questions as images is not allowed per Physics Forums rules. elfinitty, if you want further help, please re-post in a new thread with the question as readable text. The Physics Forums LaTeX features can help you to format equations.
 
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Related to Finding Shell Radius: Why (3)^1/2 - (3-y^2)^1/2?

1. What is the formula for finding shell radius?

The formula for finding shell radius is (3)^1/2 - (3-y^2)^1/2, where y represents the distance from the center of the shell to the outer edge.

2. Why is the formula for finding shell radius (3)^1/2 - (3-y^2)^1/2?

This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the radius of the shell, and the other two sides represent the distance from the center to the outer edge.

3. How is the formula (3)^1/2 - (3-y^2)^1/2 used in scientific research?

This formula is commonly used in fields related to physics and engineering, such as fluid mechanics and structural analysis. It allows scientists to calculate the radius of a cylindrical or spherical shell, which is important for understanding the behavior and properties of these structures.

4. Can the formula (3)^1/2 - (3-y^2)^1/2 be simplified or rewritten?

Yes, the formula can be rewritten as (3-y^2)^1/2 - (3)^1/2. This is simply a different way of representing the same calculation.

5. Are there any limitations to using the formula (3)^1/2 - (3-y^2)^1/2?

While this formula is useful for calculating shell radius in certain scenarios, it may not apply to all situations. For example, it assumes that the shell is a perfect cylinder or sphere and does not take into account any irregularities or variations in shape. Additionally, it may not be accurate for extremely large or small shells, as it is based on the Pythagorean theorem which is most accurate for right triangles.

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