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Math Help - Can someone just explain this to me please?

  1. #1
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    Can someone just explain this to me please?

    R is the region bounded below by y=x^2 and above by y=1. Suppose a solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of this solid.

    I know the answer is 2 (I think), but can someone explain how to do this?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See attachment -- I get 16/15
    Attached Thumbnails Attached Thumbnails Can someone just explain this to me please?-volume.jpg  
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by zhupolongjoe View Post
    R is the region bounded below by y=x^2 and above by y=1. Suppose a solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of this solid.

    I know the answer is 2 (I think), but can someone explain how to do this?
    I also get 2. Since you want the cross-sections to be perpendicular to the y-axis, it's probably best to look at this as a function of y. So we have f(y)=\pm\sqrt{y}.

    Because the length of the square goes from -\sqrt{y} to \sqrt{y}, the side length of each square is \sqrt{y}-(-\sqrt{y})=2\sqrt{y}. Thus the equation you want to integrate is:

    \int_0^1(2\sqrt{y})^2\,dy

    and this does come out to 2.

    Calculus26's math is right, but in his post he has the side lengths parallel to the y-axis, not perpendicular, and this changes the answer.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Yeah I read it wrong was thinking perpindicular to the x axis
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