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 =
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 .....
