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Semi-circle cross section volume

  1. Jun 15, 2011 #1
    1. The problem statement, all variables and given/known data

    base of a solid is bounded by y=[itex]\sqrt{x}[/itex], the x-axis, and x=9. each cross-section perpendicular to the x-axis is a semi-circle. find the volume of the solid

    2. Relevant equations



    3. The attempt at a solution
    I found the answer to be 81[itex]\pi[/itex]/16 by the following steps:
    A(semicircle)=0.5pir^2=(pi/8)*d^2 (d=diameter), and d=y=sqrt(x), so A=(pi/8)*x
    integrate (pi/8)*x from 0 to 9 (pi*9^2 /16), I get the answer as 81pi/16

    BUT the answer provided by my book is 81pi/8, did I miss something? I'm so confused and please help.
     
    Last edited: Jun 15, 2011
  2. jcsd
  3. Jun 15, 2011 #2

    Dick

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    I agree with you. Maybe we are both missing something, but I can't think what it might be.
     
  4. Jun 15, 2011 #3

    LCKurtz

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    I agree with you both.
     
  5. Jun 15, 2011 #4
    i guess the answer on my book is wrong then. I really cant think of any other ways
     
  6. Jun 16, 2011 #5

    LCKurtz

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    The book solution apparently calculated the volume assuming the cross section was a circle instead of a semi-circle.
     
  7. Jun 16, 2011 #6
    ya, that's what I think too. The thing is, my book's never wrong before (for several times I doubted its answers and it turned out it's always correct), and this is the last question for the last unit. Hopefully it's just a decoy this time hehe.
     
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