ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?
This is the Question Number 28, Exercise 17.5 of M.L Aggarwal.
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Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?
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Given speed of water flow = 15 km/h
Diameter of pipe = 14 cm
So radius of pipe, r = 14/2 = 7 cm = 0.07 m
Dimensions of cuboidal pond = 50 m × 44 m
Height of water in pond = 21 cm = 0.21 m
So volume of water in pond = 50×44 ×0.21
= 462 m3
Volume of water in pipe = r2h
= ×0.072×h
= 0.0049h
Volume of water in pond = Volume of water in pipe
462 = 0.0049h
h = 462/0.0049
= 462×7/0.0049×22
= 30000 m
= 30 km [1 km = 1000 m]
Speed = distance/ time
Time = Distance/speed = 30/15 = 2 hr
Hence the time taken is 2 hours.