A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 55 cm/s. ?

Question

(a) Express the radius r of this circle as a function of the time t (in seconds).

r(t) =

(b) If A is the area of this circle as a function of the radius, find A r.

(A r)(t) =

Answer 1

Since the circular ripple is traveling at a speed of 55cm/s; its diameter is increasing 55cm per second.

Therefore, Radius r(t) = 55/2 X t cm

                              = 55t/2 cm

                              = 27.5t cm

Also, Area (A r)(t) = pi X r² = pi X (55t/2)² cm²

                          = 2376t² cm²