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Related Rates Problem (Check work)

  1. Nov 13, 2006 #1
    A square is inscribed in a circle. As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is expanding at the rate of 8 inches per second.

    Find the rate at which the circumference of the circle is increasing.

    Perimeter = p
    diameter/diagonal = d
    circumference = C

    p = 2d sqrt2
    p = 2sqrt2 d
    dp/dt = 2sqrt2 dd/dt
    dd/dt = 8 / 2sqrt2
    dd/dt = 2sqrt2 in/sec

    C = pi d
    dC/dt = pi dd/dt
    dC/dt = 2sqrt2 pi in/sec

    Is that correct for the rate of the circumference?
    Last edited: Nov 13, 2006
  2. jcsd
  3. Nov 14, 2006 #2


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    Staff Emeritus
    Science Advisor

    Yes. I might recommend using some letter other than "d" to represent the length of the diagonal (so you don't get that "dd/dt" stuff) but you work is correct.
  4. Nov 14, 2006 #3
    OK. Thanks :)
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