Question

A stone is dropped into a lake, causing circular waves whose radii increase at a rate of 30 cm/sec.
At what rate is the area enclosed by a circular wave increasing when the radius is 50 cm.

Answer 1

\[A = \pi r^2\]\[\frac{ d }{ dt }(A) = \frac{ d }{ dt }(\pi r^2)\]\[\frac{ dA }{ dt } = \pi * 2r *\frac{ dr }{ dt } = \pi * 2 * 50 * 30 = 3000 \pi\]

Answer 2

treated r as an unknown function of t so when deriving, you mustuse product rule if it applies