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Composite Bodies: Finding the Centroid

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data
    1119614_002.jpg
    A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. Assume that the scoop of ice cream is a sphere with radius r = 3.65 cm that is placed into a 9.90 cm tall cone. The interior height of the cone is 9.00 cm. The cone has an exterior radius of 3.10 cm and an interior radius of 2.80 cm. The scoop of ice cream sits on the cone's interior radius and extends into the cone some distance. Find the z-bar centroid for the cone (the scoop of ice cream and the cone).


    2. Relevant equations
    Components: Sphere (scoop of ice-cream) and Cone (ice-cream cone)

    Volume of Sphere: V=4/3∏R3, V=4/3∏(3.65)3, V=203.6888249
    Centroid of Sphere: 12.2
    Product of Volume and Centroid: 12.2 x 203.6888249 = 2485.003664

    Volume of Cone: V=1/3∏R2h, V=1/3∏(3.10)2(9.90), V=99.62932782
    Centroid of Cone: 6.779
    Product of Volume and Centroid: 99.62932782 x 6.779 = 675.3872133

    3. The attempt at a solution
    So, z-bar = 10.40 cm (Sum of product of volume and centroid for sphere and cone/Sum of volume of sphere and cone)

    I tried that answer however, it was wrong.
    I then realised that the cone is not a completely solid shape, with it being hollow inside and that it has two different radii and height.
    As this image shows:
    1119614_003.jpg
    So, I then found the product of volume and centroid for the inner cone: volume being 73.89025921 and centroid being 6. Then, I subtracted this from the other product of volume and centroid for the cone and then found z-bar again. This was also wrong.

    I'm not sure with what else there is to do. Any help, please? I've used all the hints for the question and I only have one attempt remaining.
     
    Last edited: Oct 5, 2012
  2. jcsd
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