Then
V =
2
3
2
1
1
3
3
2
12
h
h
r h
h
π


π
=
π
=




Therefore
dV
dt  =
3
12
d
h
dh
dh
dt


π
⋅




(by Chain Rule)
=
2
4
dh
h dt
π
Now rate of change of volume, i e , V
5
d
dt =
m3/h and h = 4 m Therefore
5 =
(4)2
4
dh
dt
π
⋅
or
dh
dt  = 5
35
22
m/h
4
88
7


=
π =

π


Thus, the rate of change of water level is 35 m/h
88