SURFACE AREAS
AND VOLUMES
14 cm
25 m
22 m
Radius of pipe (R) =
7 cm
7
100
=
Length of tank (l) =
25 m
Breadth of tank (b) =
22 m
m
For pipe,
For tank,
1000 litres/hr
5000
litres
If the volume of rectangular tank is
5000 litres
If the volume of water flowing in tank in 1hr is
1000 litres
let us consider an example
Speed of water flowing through pipe
Length of water flowing in 1 hour (H)
= 5000 m
= 5 km/hr
i.e. length of water flowing in 1hr (H)
= 5 km
Height of tank (h) =
21 cm
21 m
Q. Water is flowing at the rate of 5 km per hour through a pipe of
diameter 14 cm into a rectangular tank which is 25 m long and 22 m wide.
Determine the time in which the level of water in the tank will rise by 21 cm.
(Take = 22/7)
Then, what will be the time taken ?
=
Time taken
Vol. of rectangular tank
Vol. of water flowing in 1hr
=
5
5000
1000
21
100
=
m
Q. Water is flowing at the rate of 5 km per hour through a pipe of
diameter 14 cm into a rectangular tank which is 25 m long and 22 m
wide. Determine the time in which the level of water in the tank will
rise by 21 cm. (Take = 22/7)
Sol.
=
Time taken
Vol. of rectangular tank
Vol. of water flowing in 1hr
For pipe,
H
=
5000 m,
R
=
7
100
m,
For tank,
l = 25m ,
b = 22m ,
h =
What is the formula to find
Volume of rectangle?
l × b × h
Vol. of rectangular tank
=
l × b × h
Vol. of rectangular tank
=
25
× 22
×
m3
What is the formula to find
Volume of cylinder?
π R2 H
Vol. of water flowing in 1hr
=
π R2 H
=
π
×
7
100
×
7
100
×
5000
=
π m3
∴ Vol. of water flowing in 1hr
2
49
2
21
100
m
21
100
Q. Water is flowing at the rate of 5 km per hour through a pipe of
diameter 14 cm into a rectangular tank which is 25 m long and 22 m
wide. Determine the time in which the level of water in the tank will
rise by 21 cm. (Take = 22/7)
Sol.
=
Time taken
Vol. of rectangular tank
Vol. of water flowing in 1hr
Vol. of rectangular tank
Vol. of water flowing in 1hr
Time taken
=
25 × 22 ×
=
49
2
π
÷
49
2
÷
22
7
×
2
49
×
7
22
×
21
100
25 × 22 ×
=
21
100
25 × 22 ×
=
21
100
7
3
4
2
=
3
2
=
1.5 hours
∴ The time in which the level of water in the tank will
rise by 21 cm is 1.5 hours
Vol. of water in tank = 25 × 22 × m3
Vol. of water flowing in 1hr =
π m3
49
2
21
100