a stone is thrown into a pond creating ripples that are concentric circles. the rate of change of the radius of the circle is 3 ft/min. if the radius is 0 at the time=0, how fast is the area increasing after 4 minutes

Answer 1

Radius = r
Area = 4π(r^2)

As per the question: dr/dt = 3ft/min

dr/dt = 3
When t = 4, r = t*3 = 4*3 = 12 ft

d(Area)/dt = d(4π*r^2)/dt
= 4π*2r*(dr/dt)

Plug in r = 12, dr/dt = 3, you'll get the answer (in feet squared per minute)