Volume bound by rho=2+2cos phi

[Unemployed]

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

 

[Sethric]

You are missing a sine in your volume differential. Otherwise, what is the question? What work have you done on it so far?

 

[Unemployed]

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

 

[Sethric]

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:

$$\int dV = V$$

 

[Unemployed]

just to check answer: I got 653.33 Pi.

Can anyone verify if that is correct?