MathematicsFive hundred persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04  m 3 ?  

Five hundred persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04  m 3 ?  


  1. A
    0.2cm
  2. B
    0.6cm
  3. C
    0.5cm
  4. D
    0.1cm 

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    Solution:

    Given that five hundred persons are taking a dip into a cuboidal pond. The length and breadth of the pond are 80 m and 50 m respectively.
    The formula for volume of a cuboid of length l, breadth b, and height h is given by l×b×h.
    The average displacement of the water by a person is 0.04 m 3  .
    The displacement of water by 500 persons = the rise in the volume of the pond.
    Let D denotes the displacement of water by 500 people in the pond.
    D=500×0.04 D=20 m 3  
    The displacement of water by 500 persons is 20 m 3  .
    Let the rise of water level in pond be h.
    80×50×h=20  
    h= 20 80×50 0.005m  
    The rise of water level in pond is 0.005m.
    We know that, 1 m = 100 cm.
    0.005×100=0.5   cm
    Thus, the rise of water level in the pond is 0.5cm.
    Therefore, the correct answer is option (3).
     
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