Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.

after 1 s =

after 3 s =

after 7 s =

Answer 1

given :
dr/dt = 40 cm/s

A = πr^2
dA/dt = 2π r dr/dt

case 1:
when s = 1, r = 40
dA/dt = 2π(40)(40) = 3200π cm^2/sec

case 2:
when s = 3, r = 3(4) = 120 cm
dA/dt = 2π(120)(40) = 9600π cm^2/sec

case 3:
... your turn .....

Answer 2

22400pi