Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook