Problema Solution
A welt on a person's skin is of the form of a circular region. It was found out that after reaches it's maximum size (or area in cm2), the welt decreases in diameter at a rate of 1/10 cm/min. Determine the rate of decrease in area at the instance when the diameter is measured at 1 cm.
Answer provided by our tutors
Let
x = 1 cm the diameter
x/2 = 1/2 cm is the radius
dx/dt = 1/10 cm/min the rate of decrease of the diameter
S = (x/2)^2*pi is the area
dS/dt = the rate of decrease of the area
d((x/2)^2*pi)/dt = d((pi/4)x^2) = 2pi/4*x*(dx/dt) = pi*/2*1*(1/10) = pi/20 cm^2/min
The rate of decrease in area is pi/20 cm^2/min.