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Math Help - Area and Volume

  1. #1
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    Area and Volume

    The base of a solid is a circle with radius 6. The cross sections of the solid perpendicular to a fixed diameter of the base are squares.

    If the circle is centered at the origin and the cross sections are perpendicular to the x-axis, find the area A(x) of the cross section at x and find the volume V of the solid.

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  2. #2
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    Well if the cross sections are squares then the length of each side is equal to line drawn across the circle.


    For example, at x=0, the bottom line of the area goes through the middle of the circle, so the
    area of the cross section is equal to 2(r+r)=4r=4\cdot6

    Can you visualize the shape ?

    Can you now find the term for a general x?
    Use the fact that this object is highly symmetrical.

    Hope that helps.
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  3. #3
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    So are you saying that I would need to use y= sqrt((r^2)-(x^2)) with r = 6?

    And then, would I have to multiply by 2 for the other side of the circle and finally square the entire thing to find the area equation?
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  4. #4
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    Yes that is excatly what I am saying.
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