MathematicsA well of diameter 3m is dug 14m   deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

A well of diameter 3m is dug 14m   deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.


  1. A
    0.4875m
  2. B
    0.7875m
  3. C
    0.7888m
  4. D
    0.8875m 

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    Solution:

    Given that a well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment.
    The formula for the volume of a cylinder of radius, r and height, h is given by π r 2 h  .
    The formula for the volume of a hollow cylinder of inner radius, r, outer radius, R and height, h is π R 2 r 2 h  .
    Let the height of the embankment be h.
    Radius of the cylinder is r= 3 2 m.   So, r = 1.5m
    The radius of the well is 1.5 m.
    ⇒ Volume of well =π 1.5 2 14  
    ⇒ Volume of well =31.5π m 3  
    The volume of well is 31.5π m 3  .
    The outer radius, R of embankment = inner radius + width of embankment
    = r + 5 
    = 1.5+5
    = 6.5 m
    The outer radius of the embankment is, R=5.5m.
    ⇒ Volume of embankment =π 6.5 2 1.5 2 h  
    ⇒ Volume of embankment =πh 42.252.25  
    ⇒ Volume of embankment =40πh   The volume of the embankment is 40πh  m 3  .
    Since,
    Volume of the well = the volume of embankment
      31.5π=40πh  
      h= 315 400  
      h = 0.7875 m
    Thus, the height of the embankment is 0.7875m.
    Therefore, the correct answer is option (2).
     
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