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Why surface area of sphere differ when find in two ways using the same approximation?

  1. Mar 23, 2012 #1
    i have found the area of sphere in two ways using the same approximation.but i get two different answers ;one the correct value 4∏R^2?how does this happen?
    i'm attaching the solution below?please refer to the attachments and give a solution?
     

    Attached Files:

  2. jcsd
  3. Mar 23, 2012 #2

    HallsofIvy

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    Re: Why surface area of sphere differ when find in two ways using the same approximat

    Your mistake is where "transform the frustrum to a cylinder". You don't actually do a "tranformation" you just assume frustrum is equal to the cylinder and that is not true.
     
  4. Mar 24, 2012 #3
    Last edited: Mar 24, 2012
  5. Mar 24, 2012 #4
    Re: Why surface area of sphere differ when find in two ways using the same approximat

    You write dA = 2Pirh and h = rsin(theta)dtheta, but then you write dA = 2Pir^2 sin^2(theta) dtheta. Where does the extra sin(theta) come from?
     
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