The radius of a circle grows at 3 cm/s. How fast is the circle's area increasing when the radius is 5 cm?

Core Concept

Differentiating $A=\pi r^2$ gives $\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}$. Substituting gives $2\pi(5)(3)=30\pi$ cm$^2$/s.