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Math Help - Integration General Wonder

  1. #1
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    Integration General Wonder

    Say given a semi-circle, the region is boudned by the x axis, and a solid of revolution is formed by rotation across the y axis. Then a solid of revolution is formed using also the given semi circle but bounded by both the x-axis and y-axis, and then rotated across the y axis. What is the difference in area?

    Since by visualising the solid formed, there wouldnt be a difference since the solid formed is the same. IS that correct? Or am i visuallising something wrong?
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  2. #2
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    Quote Originally Posted by Lukybear View Post
    Say given a semi-circle, the region is boudned by the x axis, and a solid of revolution is formed by rotation across the y axis. Then a solid of revolution is formed using also the given semi circle but bounded by both the x-axis and y-axis, and then rotated across the y axis. What is the difference in area?

    Since by visualising the solid formed, there wouldnt be a difference since the solid formed is the same. IS that correct? Or am i visuallising something wrong?
    if I understand your query correctly ...

    rotation of the plane region
    y = \sqrt{r^2 - x^2} about the y-axis yields a solid hemisphere of radius r.

    restricting the plane region to be rotated to that in quadrant I yields the same result.
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    The only difference being that with the semi-circle, you only have to rotate through 180 degrees to sweep out the entire volume while with the quarter circle you have to rotate throught 360 degrees.
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