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Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her 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(in minutes)?


A

80

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B

100

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C

150

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D

200

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Solution

The correct option is B

100


Let cylindrical tank be filled in x hours
Diameter of pipe = d =20 cm

Radius of pipe = r=202=10cm=0.1m

Speed of water flowing through pipe = 3 km/h = 3000 m/h

Volume of water flowing through pipe in 1 hour = π.r2.h=π×0.1×0.1×3000=30πm3

Volume of water flowing through pipe in x hours =30x.πm3

Diameter of cylindrical tank = d1=10m

Radius of cylindrical tank = r1=102=5m

Height of cylindrical tank = h1=2m

Volume of cylindrical tank = π.(r1)2.h1=π×5×5×2=50πm3
According to given condition we have:

Volume of water flowing through pipe in x hours = Volume of cylindrical tank

30x.π =50π

x=5030=53 hours=100 minutes


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