A stone is dropped into a pond, causing water waves that form concentric circles.?

Question

If, after t seconds, the radius of one of the waves is 40t cm., find the rate of change, with respect to t, of the area of the circle caused by the wave at
a) t = 1
b) t = 2
c) t = 3

Answer 1

area a = pi (radius) square = pi(40t)^2 =1600pi t^2
rate of change of area = derivative of area by t
= 3200 pi t
at
a) t is 1, area =3200 pi or 10053.1 approx
b) t is 2, area =6400 pi or 20106.19 approx
c) t is 3, area =9600 pi or 30159.29 approx

Answer 2

stone is roughly round in shape. thats why the waves are circular. if the stone is elliptical the waves would be ellipses.