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Math Help - Volume around the Axis

  1. #1
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    Question Volume around the Axis

    Hello there,

    7. Find the volume of a solid whose base is the region perpindicular to the y axis betweeen the x axis and the curve y=4-x^2, and whose perpindicular cross sections are equilateral triangles with a side that lies on the base.

    I'm really not sure what to do here. I can't find anything like this in our notes.
    Thanks for any help.
    Last edited by karisrou; May 20th 2009 at 07:03 PM.
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  2. #2
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    Quote Originally Posted by karisrou View Post
    Hello there,

    7. Find the volume of a solid whose base is the region perpindicular to the y axis betweeen the x axis and the curve y=4 - x y=4-x^2, and whose perpindicular cross sections are equilateral triangles with a side that lies on the base.

    I'm really not sure what to do here. I can't find anything like this in our notes.
    Thanks for any help.
    your problem statement is disjointed and confusing ... is that the exact wording as you read it?
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    Yeah, thats exactly as it appeared on the paper
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  4. #4
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    including the coordinate axes, please confirm that two functions are region boundaries ... the line y = 4-x and the curve y = 4-x^2
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    its just 4-x^2

    sorry, messed that up
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  6. #6
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    area of an equilateral triangle with side length "s" is

    A = \frac{\sqrt{3}}{4} s^2

    side length for each cross-section is the horizontal distance from the y-axis to the curve
    y = 4-x^2.

    using the curve's equation, solve for the horizontal distance x and use that expression in terms of y to set up an integral in the form V = \int_c^d A(y) \, dy
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