Solution The area A of a circle with radius r is given by A = πr2 Therefore, the rate
of change of area A with respect to time t is
dA
dt  =
2
2
(
)
(
)
d
d
dr
r
r
dt
dr
dt
π
=
π
⋅
 = 2π r dr
dt
(By Chain Rule)
It is given that
dr
dt  = 4cm/s
Therefore, when r = 10 cm,
dA
dt  = 2π(10) (4) = 80π
Thus, the enclosed area is increasing at the rate of 80π cm2/s, when r = 10 cm ANote  dy
dx  is positive if y increases as x increases and is negative if y decreases
as x increases Example 4 The length x of a rectangle is decreasing at the rate of 3 cm/minute and
the width y is increasing at the rate of 2cm/minute