Answer:
We have, diameter of well \[=4\text{ }m\] and height \[=14\text{ }m\]. Volume of earth taken out after digging the well \[=\frac{22}{7}\times \frac{4}{2}\times \frac{4}{2}\times 14\] \[=176\,{{m}^{3}}\] Let x be the width of the embankment formed by the earth taken out. Volume of embankment \[\frac{22}{7}[{{(2+x)}^{2}}-{{(2)}^{2}}]\times \frac{40}{100}=176\] \[\Rightarrow \frac{22}{7}[4+{{x}^{2}}+4x-4]\times \frac{2}{5}=176\] \[\Rightarrow {{x}^{2}}+4x=\frac{176\times 5\times 7}{22\times 2}\] \[\Rightarrow {{x}^{2}}+4x-140=0\] \[\Rightarrow {{x}^{2}}+14x-10x-140=0\] \[\Rightarrow x(x+14)-10(x+14)=0\] \[\Rightarrow (x+14)(x-10)=0\] \[\Rightarrow x=-14\,\,\] or \[10\] \[x=-14\] (neglect) \[\therefore x=10\] Hence, width of embankment \[=10\text{ }m\].
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