A burn on a person’s skin is in the shape of a circle. If the radius of the burn is decreasing at the rate of 0.05 cm per day when it is 1.0 cm, what is the rate of decrease of the area of the burn at that instant?
A for area, t for time in days, r for radius in cm
A=pi*r 2
dA/dr = 2*pi*r
dr/dt = -0.05
dA/dt = (dA/dr) * (dr/dt) = 2*pi*r * -0.05 = -0.1*pi*r
When r=1,
dA/dt = -0.1*pi*1 = -0.1pi = -0.314
The instantaneous decrease in area is approx 0.314 cm 2/day
+118654 
