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Dimensional analysis. Please check my working

  1. Mar 27, 2014 #1
    1. The problem statement, all variables and given/known data
    Two spheres are cut from a certain uniform rock. One has radius 4.30 cm. The mass of the other is six times greater. Find its radius.


    2. Relevant equations
    v = (4/3)(pi)(r)^3
    m = vp


    3. The attempt at a solution
    6[(4/3)(pi)(r1)3] = (4/3)(pi)(r2)3
    8(pi)(r1)3 = (4/3)(pi)(r2)3
    6(r1)3 = (r2)3
    6(4.3)(1/3) = 9.7568

    Answer:
    9.76 cm

    I got this question wrong for some reason... Where is my mistake...?
     
  2. jcsd
  3. Mar 27, 2014 #2

    rude man

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    Going from 2nd last to last equation you made your basic mistake.
     
  4. Mar 27, 2014 #3
    I don't see it... :(
     
  5. Mar 27, 2014 #4

    SteamKing

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    If you take a sphere with radius r, and make another sphere with radius 2*r, what is the ratio of the volume of the bigger sphere to the smaller sphere?
     
  6. Mar 27, 2014 #5

    rude man

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    Take the cube root of each side. Your mistake is on the left-hand side.
    Fact: (ab3)1/3 = a1/3b
     
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