Question

A well 14 m inside diameter is dug 15 deep. Earth taken out is spread all around to a width of 7 m to from an embankment . Find the height of the embankement .

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Answer 1

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$\bf \scriptsize{Volume \: of \: earth \: dug \: out = \: \pi \times r^{2} \times h} \\ \bf \scriptsize{ \implies \frac{22}{7} \times ( \frac{14}{2}^{2} ) \times 15 \: m^{3}} \\ \bf \scriptsize{Area \: of \: the \: embankment \: ( Shaded \: portion) = \pi \: R^{2} - r^{2} }$

$\bf \scriptsize{ \implies \frac{22}{7} [(14)^{2} - (7)^{2} ]} = \frac{22}{7}(196 - 49) = 462 \: m^{2}$

$\bf \scriptsize{Height \: of \:the \: earth \: dug \: out = \frac{volume \: of \: the \: earth \: dug \: out}{area \: of \: the \: \: embankmemt} = \frac{ \cancel{2310}}{ \cancel{462}} = 5 \: m. }$

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