The radius of a circular puddle is increasing at a rate of 2 cm/s. How fast is the area of the puddle increasing when the radius is 10 cm?

Core Concept

We know that A = πr². Differentiating with respect to time t: dA/dt = 2πr(dr/dt). Given dr/dt = 2 cm/s and r = 10 cm: dA/dt = 2π(10)(2) = 40π cm²/s.