Related Rates Problem (Check work)

[sportsguy3675]

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?

 

[HallsofIvy]

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.

 

[sportsguy3675]

OK. Thanks :)