A well of diameter 4m is …

According to the question,the well of diameter 4 metre is dug 14 metre deep.
We are given that, Depth of well = 14 m, radius = 2 m.
Volume of earth taken out {tex}= \pi r ^ { 2 } h{/tex}

{tex}= \frac { 22 } { 7 } \times 2 \times 2 \times 14{/tex}

{tex}= 176 m ^ { 3 }{/tex}

Let r be the width of embankment,then

the radius of outer circle of embankment = 2 + r

Area of upper surface of embankment {tex}= \pi \left[ ( 2 + r ) ^ { 2 } - ( 2 ) ^ { 2 } \right]{/tex}

Volume of embankment = Volume of earth taken out

or, {tex}\pi \left[ ( 2 + r ) ^ { 2 } - ( 2 ) ^ { 2 } \right] \times 0.4 = 176{/tex}

or, {tex}\pi[4 + r^2 + 4r-4] \times 0.4 = 176{/tex}

or, {tex}r ^ { 2 } + 4 r = \frac { 176 \times 7 } { 0.4 \times 22 }{/tex}

or, {tex}r ^ { 2 } + 4 r = 140{/tex}

or, {tex}r ^ { 2 } + 4 r - 140 = 0{/tex}

or, {tex}( r + 14 ) ( r - 10 ) = 0{/tex}

or, r = 10 m  [as radius can't be negative]

Hence width of embankment = 10 m.