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Math Help - Rate of Change Problem

  1. #1
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    Feb 2010
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    Rate of Change Problem

    Hi, I was just wondering if someone could tell me if I am doing the following problem correctly?

    The vertices of a square are moving away from the centre at a rate of 2 cm/s. How fast is the area of the inscribed circle changing when the side of the square is 20 cm?

    I let r=10 cm and plugged it into the derivative of the area of a circle... is this what I am supposed to do?

    Thanks for any help
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  2. #2
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    Joined
    Nov 2009
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    r - radius of inscribed circle at start
    a - side of square at start;

    r=a/2, you spotted that well.

    Now "The vertices of a square are moving away from the centre at a rate of 2 cm/s ", what that means actually?

    Spoiler:
    That means the diagonal of the rectangle is increasing by 2x of both sides, where x is s, as you stated


    Here is the calculation of the side of the rectangle:

    Spoiler:

    2x+a*\sqrt{2}+2x=4x+a*\sqrt{2}

    z - the side of rectangle after s passed

    (4x+\sqrt{2}*a)^2=2z^2
    (4x+\sqrt{2}*a)=\sqrt{2}z
    4x/\sqrt{2} + a = z



    Now what is r after?

    Spoiler:

    r_{after}=2x/\sqrt{2} + a/2


    Finally,

    A=r^2_{after}*\pi

    Regards.
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