Question

Area the radius, r, of a circle is decreasing at a rate of 3 centimeters per minute. find the rate of change of area, a, when the radius is

Answer 1

A = pi r^2
dA/dr = 2 pi r
dr/dt = -3 (given)

rate of change of the area = dA/dt = dA/dr / rd/dt = 2 pi r / -3 = -2/3 pi r