MathematicsIn the middle of a rectangular field measuring 30 m×20 m,   a well of 7 m diameter and 10 m   depth is dug. The earth so removed is evenly spread over the remaining part of the field. What is the height through which the level of the field is raised?

In the middle of a rectangular field measuring 30 m×20 m,   a well of 7 m diameter and 10 m   depth is dug. The earth so removed is evenly spread over the remaining part of the field. What is the height through which the level of the field is raised?


  1. A
    68.5 cm
  2. B
    68.6 cm
  3. C
    68.7 cm
  4. D
    68.8 cm 

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    Solution:

    It is given that,
    Measure of rectangular field = 30 m×20 m,   the diameter of well (d) = 7m and depth (h) =10m.
    We know that,
    Radius= Diameter 2  
    So, Radius of well r=72m.
    Since, the volume of cylinder =π r 2 h  . Then, volume of earth dug is,
    = 22 7 × 7 2 2 ×10 = 22 7 × 7 2 × 7 2 ×10  
    =385 m3.
    Since, measure of rectangular field = 30 m×20 m,  
    Thus, the area of field is,
    =l×b =30×20 =600 m 2  
    Area of circle =π r 2  .
    The area of well is,
    =π r 2 = 22 7 × 7 2 × 7 2 = 77 2 m 2  
    Now, the area of the remaining field is,
    = Total area of the field - Area of well
    =60038.5 =561.5 m 2  
    Thus, the height through which the level of the field is raised is,
    = Volume of earth Area of field = 385 561.5 = 385×10 5615 =0.6856m =68.56cm  [1 m = 100 cm]
    Thus, the height through which the level of the field is raised is 68.56, rounded off to 68.6 cm.
    Therefore, option 2 is correct.
     
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