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Math Help - Rotational Vol Question.

  1. #1
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    Rotational Vol Question.

    IŽll try to explain this problem. Trying to solve this for the last 40minutes now.


    Equation: y = x^(0,5)

    The area under this equation starts to rotate around the X-axis and gives you the rotational Volume (B).

    When calculating the above mentioned volume: Int: from (a = 0) to (b), There is a line from the point b parallell to the X-axis ( called line d), that line crosses the y-axis. The area between: Y-axis; This line (d), and the area "above" the y = x^0,5 graph starts to rotate around the y axis. This gives you volume (A).

    Find x when these areas have the same volumes ( A = B).

    The equation for calculating volume rotating around X-axis is:
    INT: (pi)*(y^2):dx from a to b (on the x-axis as limes a = 0)

    The equation for calculating volume rotating around y-axis is: Int:2*pi*xy:dx from a to b (on the X-axis ALSOOO).

    At first I thought, never mind the rotation, just solve so the areas a equal, but that was not very clever, points further from the axises give larger values for volume then closer points do.

    I keep getting the answer x = 0,625^2 but that is wrong, THE CORRECT SOLUTION IS (6.25;2.5)
    Hope I discribed this problem understandably.
    Last edited by Henryt999; January 8th 2010 at 02:13 PM.
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  2. #2
    MHF Contributor ebaines's Avatar
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    It's a little difficult following what you mean - partly because you talk about the "area" of A whereas I think you mean "volume," and also because I don't know what the "a" value is supposed to signify. Is "a" = 0? And when you ask for the value of x, do you mean the value of b to make the two volumes equal?

    I will assume that the problem is to find a value for b such that the volume B (which is the defined by rotating y = sqrt(x) about the x axis, and finding the volume from x = 0 to x = b) is equal to the volume A (defined as rotating y = sqtr(x) about the y axis, and finding the volume from y = 0 to y = sqrt(b). If I have that right, then the answer for b turns out to be 6.25. I can help you thorugh this, but before I do please verify that I have interpreted the problem correctly.
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  3. #3
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    You are right

    Yes, you are correct, my mistake talking about the areas when the question was about volume. Please How did you get the answer?
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  4. #4
    MHF Contributor ebaines's Avatar
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    Given the function y = sqrt(x): the volume of B is:

    <br />
B = \int _ 0 ^b y^2 dx = \int _0 ^b x dx = \frac {b^2} 2<br />

    The volume of A is:
    <br />
A = \int _0 ^{\sqrt b} x^2 dy = \int _0 ^{\sqrt b} y^4 dy = \frac 1 5 (\sqrt b) ^5 = \frac 1 5 b^{ \frac 5 2}<br />

    Set volume A = volume B, and solve for the value of b.
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  5. #5
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    T

    That was nice and simple
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