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Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.


Solution

Inner diameter of well =14 m

Inner radius =142=7m

Depth (h)=12 m

Volume of earth dig out =πr2h

=227×(7)2×12m3

=227×7×7×12m3=1848m3

Width of the embankment of the well =7 m

Outer radius (R)=7+7=14 m.

Let height of the embankment =h

Volume =πR2h=πr2h

=πh(R2r2)=227h(R2r2)

227h(14272)=1848

227(14+7)(147)=1848

227h×21×7=1848

462h=1848

h=1848462=4

Height of embankment =4 m

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