Solution Let r be the radius of the given disc and A be its area Then
A = πr2
or
dA
dt  = 2
dr
πr dt
(by Chain Rule)
Now approximate rate of increase of radius = dr = 
0 05
dr
t
dt ∆ =
cm/s Therefore, the approximate rate of increase in area is given by
dA =
A (
)
d
dt ∆t
 = 2
rdr
t
dt


π
∆




= 2π (3