An agriculture field is in the form of a rectangle of length 20 m, and width 14 m. A 10 m deep well of diameter 7 m is dug in a comer of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level of the field. - Zigya
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An agriculture field is in the form of a rectangle of length 20 m, and width 14 m. A 10 m deep well of diameter 7 m is dug in a comer of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level of the field.


Since shape of the well is just like the shape of cylinder, so we consider well as cylinder.
Let r m be the radius and h m be the height of the well, then 
straight r space equals fraction numerator 7 degree over denominator 2 end fraction straight m comma space straight h space left parenthesis depth right parenthesis space equals space 10 straight m
Now,
Volume of earth dug out = πr squared straight h

                          equals space open parentheses 22 over 7 x 7 over 2 x 7 over 2 x 10 close parentheses m cubed equals 385 space m cubed
Also, we have, 
Length of the rectangular field = 20 m
Breadth of the field = 14 m
Therefore, are of the field = (20 x 14) m2
                                      = 280 m2
And
   Area of the remaining part of the field
               = Area of field - Area of the base
                 
                     equals space open parentheses 280 minus 77 over 2 close parentheses straight m cubed
Since,
Volume of the raised field
         = Volume of the earth dug out
rightwards double arrow space space open parentheses 483 over 2 close parentheses straight h space equals space 358
rightwards double arrow space space space straight h space equals space fraction numerator 358 space straight x space 2 over denominator 483 end fraction
rightwards double arrow space space space straight h space equals space 1.6 space left parenthesis approx right parenthesis
Hence, rise in the level of the field = 1.6 m (apporx.)

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