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# Finding density using multiple integrals

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1. For this question, I used the formula:
M=∫ρ dV where M=mass and ρ=density=cos²θ. I converted this into spherical co ordinates and integrated to obtain M=4πR³/9 . How do I find the density from this? The answer is ρ=9M/4πR³ but I am not sure how this was obtained
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2. (Original post by bobbricks)
For this question, I used the formula:
M=∫ρ dV where M=mass and ρ=density=cos²θ. I converted this into spherical co ordinates and integrated to obtain M=4πR³/9 . How do I find the density from this? The answer is ρ=9M/4πR³ but I am not sure how this was obtained
Question says , not equal to.

Lets say

So, using we can determine the constant k.

At Z, theta=0, so density at Z is simply k, whatever that works out to be.
3. (Original post by ghostwalker)
Question says , not equal to.

Lets say

So, using we can determine the constant k.

At Z, theta=0, so density at Z is simply k, whatever that works out to be.
So k=9M/4πR³ and density=kcos^2(theta) and at z=0, theta=0 so density=k. Makes sense, thanks!
4. (Original post by bobbricks)
So k=9M/4πR³ and density=kcos^2(theta) and at z=0, theta=0 so density=k. Makes sense, thanks!
Yep. Though it's not the case z=0, rather, at Z we have theta=0....

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