MathematicsWater is flowing at the rate of 15 km/h   through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Water is flowing at the rate of 15 km/h   through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?


  1. A
    2 hours
  2. B
    3 hours
  3. C
    1 hours
  4. D
    4 hours 

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    Solution:

    Given that rate of flowing of water is 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide.
    Let the time per hour rise of water in the pond be t hour.
    Radius of pipe = 14 2   = 7cm.
    We know that,
    1 cm = 1100m
    So, radius of pipe = 7 100 =0.07m  .
    Rate of flow = 15 km/h
    We know that, 1 km = 1000 m
    Rate of flow = 15(1000) m/h = 15000 m/h
    Volume of water flowing through the cylindrical pipe in one hour = π r 2 h  .
    V= 22 7 ×0.07×0.07×15000 V= 1617 7 V=231 m 3  
    Volume of cuboidal pond = length × width × depth
    Here,
    Length = 50 m
    Width = 44 m
    Depth = 21 cm
    We know that,
    1 cm = 1100m
    So, depth = 21 100 =0.21m  
    ⇒ Volume of pond = 50 × 44 × 0.21
    ⇒ Volume of pond = 462 m³
    Now,
    Time taken by the pipe to fill the pond with water to a height of 21 cm is,
    T= Volume of pond Volume of water flowing through the pipe in one hour  
    T= 462 231 T=2 hours  
    Therefore, water in the pond will rise by 21 cm in 2 hours.
    Therefore, the correct answer is option (1).
     
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