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Volume of a sphere with a hole

  1. Oct 10, 2006 #1

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    http://i12.tinypic.com/2yljjif.jpg

    A goldsmith makes a wedding band by taking a gold ball and drilling a wide hole through it. The wedding band has to be 1 cm wide and the hole has to have a diameter of 2 cm.

    Given that gold weighs 19.32g/cm^3, how heavy will the wedding band be?

    does 2.529 g seem like the correct answer?
     
  2. jcsd
  3. Oct 10, 2006 #2

    arildno

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    Haven't the faintest idea. Show your work, and we'll be the judges.

    However:
    For goodness sake, spare us the figures, set up and solve the problem IN SYMBOLS!
     
  4. Oct 10, 2006 #3

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    x^2 + y^2 = (1/2)^2 + (1)^2 = 5/4
    x^2 = 5/4 - y^2

    The volume of wedding band

    = pi integral{-1/2 to 1/2} [(5/4 - y^2) - (1^2)] dy

    = pi integral{-1/2 to 1/2} (1/4 - y^2) dy

    = pi [y/4 - (1/3)y^3]

    = pi /24 cm^3

    mass=(pi/24)(19.32) = 2.529 g

    is this correct?
     
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