Let A(t) be the (changing) area of a circle with radius r(t), in feet, at any time t in min.

Question

If the radius is changing at the rate of dr/dt =3ft/min, find the rate of change
of the area(dA/dt) at the moment in time when r = 16 ft

dA/dt=

Answer 1

A = πr^2
dA/dt = 2πr dr/dt

so when r = 16 ft and dr/dt = 3 ft/min

dA/dt = 2π(16)(3) ft^2/min
= 96π ft^2/min