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Volume of Rotation

  1. Aug 30, 2007 #1

    danago

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    Find the volume of the solid generated by rotating the region trapped between the curve y3=x2, the y-axis, the line y=4 and the line x=0 around the y-axis.

    I started by writing x as a function of y, explicitly:

    [tex]x=y^{1.5}[/tex]

    Heres the graph i obtained, with the shaded area being the area to be rotated about the y axis.

    [​IMG]

    [tex]
    V = \pi \int\limits_0^4 {(y^{1.5} )^2 dy = } \pi \int\limits_0^4 {y^3 dy = } 64\pi {\rm{ units}}^3
    [/tex]

    The answer in the book says it should be 631.65 units3. It looks to me as if they multiplied by [tex]\pi^2[/tex] instead of just [tex]\pi[/tex]. Am i missing something, or am i on the right track?

    Thanks in advance,
    Dan.
     
  2. jcsd
  3. Aug 30, 2007 #2

    Dick

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    It looks like 64*pi units to me as well. Are we both missing something?
     
  4. Aug 30, 2007 #3
    i got the same answer and i haven't solved any volume problems in a long time
     
  5. Aug 30, 2007 #4

    Dick

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    That concludes it. The score is 3 against 1. The book answer is wrong. Not all that unusual.
     
  6. Aug 31, 2007 #5

    danago

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    Alright thats good to hear :smile: Thanks for confirming it guys :smile:
     
  7. Aug 31, 2007 #6
    Is it a solutions manual or the back of the book?

    They did square pi but I dont see how they did. I wonder if they thought that pi should be squared because the radius (R(x)) is squared which is completely wrong. Quite strange really.
     
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