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.

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