water is flowing at 15km/h through a pipe of diameter 14cm into a rectangular tank which is 50m long and 44m wide. find the time in which the level of water in the tank will rise by 21 cm
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Answer:
Let the length of the pipe for filling the whole tank be h m.
(i) pipe is in the form of cylinder where height =h m
diameter =14 cm
⇒=
2
14
=7cm=
100
7
m
Volume of pipe = volume of cylinder =πr
2
h
⇒πr
2
h=π(
100
7
)
2
h=
7
22
×
100
7
×
100
7
×h=
100×100
22×7h3
(ii) Tank is in the form of caloid where l=500m
b=44m,h=21cm=
100
21
m=0.21m
Volume of the tank =lbh=50×44×
100
21
=22×21m
2
We have volume of pipe = volume of tank
⇒
100×100
22×7h
=22×21
⇒h=3×10000m=
1000
30,000
km=30km
Water in pipe flows at the rate of 15km/hr
30km travels in pipe in
15
30
hrs=2hrs
So, in 2hrs, the tank will be filed.
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