Question

the radius of a circular puddle is growing at a rate of 20 cm/s. How fast is the area growing at the instant when it equals 25 cm^2? (use the area formula to determine the radius at that instant)

Answer 1

So, we have that
\[A = \pi r^2\]
so the time derivative of the area is, via the chain rule,
\[\frac{dA}{dt} = 2\pi r \cdot \frac{dr}{dt} \]