Since the plate is circular, therefore the area of the plate is jut equal to the area of a circle, so:
Area of plate = πr² = A
Taking the derivative:
dA / dr = 2πr --->
1
By
the idea of partial differentiation, the equation can also take in the form of:
dA/dt = dA/dr x dr/dt ---> 2
Where
we are given that:
change in radius over time = dr/dt = 0.02 cm/min
change in area with changing radius = dA/dr = 2πr ---> from equation 1
at r = 40
dA/dr = 2π(40) = 80π
Substituting
all the known values into equation 2:
dA/dt = (80π)(0.02)
dA/dt = 1.6π cm^2 /s = 5.03 cm^2/s
