Volume bound by rho=2+2cos phi

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Homework Help Overview

The discussion revolves around finding the volume bounded by the equation ρ = 5 + 2cos(φ). Participants are exploring the geometric interpretation and limits of integration for the volume calculation in spherical coordinates.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the volume differential and the necessary limits for integration, with some questioning the visualization of the object defined by the equation. There are attempts to clarify the correct expression for the volume differential and the limits for φ and θ.

Discussion Status

The discussion is ongoing, with participants providing corrections and suggestions regarding the limits of integration. Some guidance has been offered about the bounds for φ and θ, but there is no explicit consensus on the final volume calculation.

Contextual Notes

There is a noted typo in the volume differential, and participants are working under the constraints of homework rules, which may limit the depth of exploration into the visualization of the object.

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Homework Statement



Find the volume bounded rho=5+2cosphi

Homework Equations


dV=rho squared drho d phi d theta



The Attempt at a Solution



I am guessing this is some cylindrical shape. Theta should be 0-2pi and phi=0 pi/2
 
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You are missing a sine in your volume differential. Otherwise, what is the question? What work have you done on it so far?
 


ok typo: dV= rho squared sin phi drho dphi d theta

I cannot visualize this object to find the volume bound by rho= 5+2cos(phi)

I want to know the limits of dtheta and dphi

Integrating rho squared is easy
I am guessing the limits are 0-pi/2 for phi
and 0-2pi for theta
 
You will need to go all the way to pi for phi. Your theta bounds are correct. You don't need to worry about visualizing it - you know the volume differential:

\int dV = V
 
just to check answer: I got 653.33 Pi.

Can anyone verify if that is correct?
 

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