Question

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

Answer 1

dr/dt=30
area=pi*r^2
rate of change of area
d(area)/dt=pi*2*r*dr/dt=pi*2*r*dr/dt
dr/dt=30
d(area)/dt=2*pi*30*r=60*pi*50=3000*pi

Answer 2

circumference=2*pi*r
rate of change=dc/dt=2*pi*dr/dt=2*pi*30=60pi

Answer 3

@sarcos11