The Area of a circle increases at a rate of 1 cm^2/s. How fast is the radius changing when the circumference is 2 cm?

The area of a circle:

A = πr²

dA/dr = 2πr

We are given dA/dt, using the chain rule

dr/dt = dA/dt x dr/dA

dr/dt = 1 x 1/2πr

When circumference = 2 cm:

2 = 2πr

r = 1/π; putting this value of r

dr/dt = 1/2π (1/π)

dr/dt = 1/2 cm/s

The radius is increasing at a rate of 1/2 cm/s.