Let A be the area of a circle with radius r that is increasing in size with respect to time. If the rate of change of the area is 8 cm/s, find the rate of change of the radius when the radius is 3 cm.

Answer 1

ah, a nice related-rates problem.

a = pi r^2
da/dt = 2pi r dr/dt
when r=3,
8 = 2pi(3)(dr/dt)
dr/dt = 4/(3pi) cm/s

By the way, da/dt is 8 cm^2/s. That makes the units come out right.

cm^2/s = 2pi(cm)(cm/s)