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Water is flowing at the rate of $3 km / h$ through a circular pipe of $20 cm$ internal diameter into a circular cistern of diameter $10 m$ and depth $2 m$ . In how much time, will the cistern be filled?

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70min

110min

100min

90min

answer is C.

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Detailed Solution

Given that the dimensions are,
Diameter of the pipe (d) =20 cm
Radius of the pipe (r) = 10cm = 0.1m (1m=100cm)
Radius of circular cistern,

R = 102 = 5 m

Depth of cistern (H) =2m
We have the following formula,
Volume of the cistern

= π R 2 H

The volume of the cistern will be,

= 227 × (5) 2 × 2 = 11007 m 3

Then the volume of water flowing through pipe will be the same as the volume of cistern,

227 (0.1) 2 × h = 11007 h = 11007 × 722 × 1 (0.1) 2 = 5000 m

The water is flowing at rate of 3km / h,
Then in 60 minutes, the length of water flowing = 3 km = 3000m (1km=1000m,1min=60s)
Then, 5000 m length of water will be flowing in time,

= 603000 × 5000 = 100 min

Thus the time taken will be 100 min. Therefore the correct option is 3.

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