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Find the centroid of the solid in part (a).

  1. Dec 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid that lies above the cone
    ϕ=pi/3
    and below the sphere
    ρ=4cosϕ
    .

    2. Relevant equations

    Find the centroid of the solid in part (a).


    .
    3. The attempt at a solution

    For the volume I got 10pi which I am fairly sure is correct. I attempted trying to calculate the centroid and i got a different answer from the book. I have (0,0,21/40)

    and I would like to know what did i do incorrect. I calculated ybar and xbar and i got 0.
    for zbar, i did the following

    ∫0→pi/3∫0→2pi∫0→4cosϕ (ρ^3cosϕsinϕdρdθdϕ)


    the book's answer for the inner integration of rho was ∫0→2pi∫0→pi/3 (cosϕsinϕ(64cos^4(ϕ))dϕdθ

    is this correct? isnt supposed to be ∫0→2pi∫0→pi/3 (cosϕsinϕ(64cos^4(ϕ)/4)dϕdθ?

    or am I wrong? (I divided by 4, because that's the rule of integration)
     
  2. jcsd
  3. Dec 8, 2012 #2

    Dick

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    Science Advisor
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    Re: Centroid

    You get (4cosϕ)^4/4, right? What's 4^4/4?
     
  4. Dec 8, 2012 #3
    Re: Centroid

    hahaha!I fell so dumb now. Making very stupid mistakes. thanks for output!
     
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