Volume of a Solid: Solve Problem with Washer/Shell Method

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Homework Help Overview

The discussion revolves around finding the volume of a solid formed by rotating a region defined by the curves y=x^2, y=0, x=2, and x=4 about the line x=7. Participants are exploring methods to calculate this volume using the washer and shell methods.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply both the washer and shell methods but expresses confusion regarding the setup, particularly the inner and outer radii and the bounds of integration. Other participants suggest showing attempts to identify errors and clarify the integration process.

Discussion Status

Some participants have provided guidance on the setup of the shell method, indicating that the radius should be calculated as 7-x instead of just x. There is an acknowledgment of differing results regarding the final volume, with one participant asserting correctness based on an online homework system.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may impose specific methods or approaches to be used. There is a focus on ensuring the correct interpretation of the problem setup and integration limits.

willson.slp
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I'm have trouble with a homework problem having to do with find volume of an area. the problem reads:

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x^2 , y=0 , x=2 , x=4;


about the line x=7

I've tried using the washer method and also the shell method with no luck. Any help would be greatly appreciated.

Thanks
 
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Show your attempt, please, so as we can find out what went wrong.

ehild
 
since its rotating about the line x=7, I solved for y first

Im using pi*intergral from 0 to 16 of ((7-sqrt(y))^2-(7-5)^2)dy

I think I'm messing up with what my inner and outer radius' are and possibly the bounds
 
Last edited:
Y goes from 0 to x^2. First I would get the volume of a cylindrical shell of radius 7-x, thickness dx and height y=x^2. Then the integration with respect to x goes from x=2 to x=4.

ehild
 
Last edited:
That did it!
I came up with 424pi/3

When I initially tried the shell method I was using just x for the radius instead of 7-x. Thanks again for the help!
 
Is not it 436pi/3?

ehild
 
I double checked it and still got 424pi/3
The homework is online and I got it correct
 

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