Using polar coordinates to find the volume of the given solid

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Homework Help Overview

The discussion revolves around finding the volume of a solid defined by being inside a sphere and outside a cylinder, utilizing polar coordinates for the calculation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the setup of a double integral to calculate the volume, with specific limits for the polar coordinates. There is a focus on ensuring the limits correctly reflect the region outside the cylinder.

Discussion Status

Some participants have confirmed the correctness of the integral setup, while others have raised questions about the limits of integration, indicating a productive exploration of the problem.

Contextual Notes

There is an emphasis on showing effort before seeking help, as indicated by one participant's request for prior attempts to be shared.

serg_yegi
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1. Use polar coordinates to find the volume of the given solid.
2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
 
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serg_yegi said:
1. Use polar coordinates to find the volume of the given solid.



2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
What have you tried? You have to show an effort first.
 
I've tried doing a double integral from theta=0 to theta=2pi and r=0 to r=4 of ((16-r^2)^(1/2))r (dr)(dtheta)
 
The limits of integration for r should be from r = 2 to r = 4. If you go from r = 0, you're getting the volume inside the cylinder, which you don't want.
 
Ok. Is the actual integral correct?
 
Yes, I don't see anything wrong with it.
 

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