MathematicsA well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form a 40cm high embankment. Find the width of the embankment.

A well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form a 40cm high embankment. Find the width of the embankment.


  1. A
    5.48m
  2. B
    7.48m
  3. C
    6.48m
  4. D
    8.48m 

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    Solution:

    Given,
    Well diameter = 4m and,
    The depth of the well is = 14m
    The height of the embankment form is = 40 cm.
    Step 1: As mentioned in the question, the excavated soil is spread evenly over the borehole to form a 40cm high embankment from the well, the excavated soil is spread evenly over the entire borehole to form a 40cm high embankment. So we need to find the volume of the well, but to find the volume we need to recognize the shape because we know that the well is cylindrical in shape. So first we need to find the radius of the well.
    Diameter of the well = 4m
    As we know, the radius is equal to half the diameter.
    The radius of the well Radius of the well = 2m
    Step 2: Now we can find the volume of the well using the formula (1) as given in the solution hint.
    As stated in the query, the depth of the well is 14m and the radius is 2m.
    Volume of the well =π (2) 2 ×14   
    Volume of the well = 22 7 ×4×14  
    Volume of the well =22×8  
    Volume of the well =176 m 3  
    Step 3: Now we find out the volume of the embankment. In order to determine the volume, we must first recognize the shape of the excavated soil, which is spread evenly throughout the borehole to form a 40 cm high embankment. As we know, the shape of the embankment is in the shape of a cylinder. However, to find out the volume, we must first convert the height of the embankment in m.
    as we know
    1 m = 100 cm
    Hence, height of the embankment = 40 100 m  
    Height of the embankment =0.4m  
    Hence, Volume of embankment =π× (r) 2 ×0.4  
    Hence, Volume of embankment = 22 7 × (r) 2 ×0.4 m 3  
    Step 4: Now as it is stated in the question that the earth is excavated to form an embankment, we can say that the volume of the dug well is equal to the volume of the embankment form. By comparing the volume of the well and the volume of the embankment, we can therefore determine the width of the embankment.
    22 7 × r 2 ×0.4=176  
    r 2 =176× 7 22 r 2 =56 r= 56 r=7.48m  
    Hence, width of the well is, 7.48m
     
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