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Homework Help: Mass from density

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the mass of the following object with the given density function:

    The ball of radius 8 centered at the origin with a density f(ρ,ϕ,θ) = 2e^-p^3

    2. Relevant equations

    3. The attempt at a solution
    I know that I need to integrate the density function, but I'm not sure what limits to use. My book tells me that a sphere with radius a centered at the origin has the description: {(ρ,ϕ,θ): p=a}, a>0. However, I'm not exactly getting how this helps me find the limits.
  2. jcsd
  3. Apr 10, 2012 #2


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    Do you understand spherical coordinates? Can you describe the ranges the three variables ##\rho,\ \phi,\ \theta## must traverse to sweep out a sphere of radius ##a## centered at the origin?
  4. Apr 10, 2012 #3
    Would the limits be:

    for ρ 0 to 8

    for θ 0 to 2pi

    and for ϕ 0 to pi?

    If not, I need to review spherical coordinates.
  5. Apr 10, 2012 #4


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    That's right, and you just answered your own question about what limits to use.
  6. Apr 10, 2012 #5
    Thank you. Sometimes when you have a lot on your mind it's easy to forget simple things. :P
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