SURFACE AREAS
AND VOLUMES
20 cm
10 m
2 m
Speed of water flowing through pipe
Radius of pipe (r) =
10 cm
1
10
=
Sol.
Radius of tank (R) =
5 m
10
2
=
Height of tank (H) =
2 m
m
Length of water flowing in 1 hour (h)
= 3000 m
= 3 km/hr
Q. A farmer connects a pipe of internal diameter 20 cm from a canal into a
cylindrical tank in his field, which is 10 m in diameter and 2 m deep.
If water flows through the pipe at the rate of 3 km/h, in how much time will
the tank be filled?
let us consider an example
i.e. length of water flowing in 1hr (h)
= 3 km
1000 litres/hr
5000
litres
Then, what will be the time taken ?
=
Time taken
Vol. of cylindrical tank
Vol. of water flowing in 1hr
=
5
5000
1000
If the volume of cylindrical tank is
5000 litres
If the volume of water flowing in tank in 1hr is
1000 litres
=
Time taken
Sol.
Q. A farmer connects a pipe of internal diameter 20 cm from a canal into a
cylindrical tank in his field, which is 10 m in diameter and 2 m deep.
If water flows through the pipe at the rate of 3 km/h, in how much time will
the tank be filled?
R
=
5 m,
H
=
2 m,
r
=
1
10
m,
h
=
3000 m
What is the formula to find
Volume of cylinder?
π R2 h
Vol. of water flowing in 1hr
=
π r2 h
=
π
×
1
10
×
1
10
×
3000
=
(30π) m3
Vol. of cylindrical tank
=
π R2 H
=
π
×
25
×
2
∴ Vol. of water flowing in 1hr
∴ Vol. of cylindrical tank
Vol. of cylindrical tank
Vol. of water flowing in 1hr
π r2 h
=
50 π m3
=
Time taken
Vol. of cylindrical tank
Vol. of water flowing in 1hr
Q. A farmer connects a pipe of internal diameter 20 cm from a canal into a
cylindrical tank in his field, which is 10 m in diameter and 2 m deep.
If water flows through the pipe at the rate of 3 km/h, in how much time will
the tank be filled?
Sol.
Vol. of cylindrical tank
Vol. of water flowing in 1hr
Time taken
=
50π
=
30π
Time taken to fill the tank is 100 minutes.
=
5
3
× 60
20
=
100 minutes
Vol. of water in tank = 50 π m3
Vol. of water flowing in 1hr = 30 π m3
5
=
3
∴