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 .....