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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
    and below the sphere

    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


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    Homework Helper

    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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