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Question
A well with 14m diameter is dug 21m deep. The earth taken out of it has been evenly spread all around it to a width of 14m to form an embankment. Find the height of the embankment.
Solution
The shape of the well will be cylindrical.
Depth (h1) of well = 21m
Diameter of the well = 14m
Radius (r2) of well = 14m
Width of embankment (r2)
= 7m + 14m
= 21m
Let height of the embankment be h2
Volume of earth spread on the embankment
= πh2(r22 - r12)
= rh2(r2 + r1)(r2 - r1)
= `(22)/(7) xx "h"_2 xx 28 xx 14`
= 1232h2
Volume of soil dug from well = Volume of earth used to form embankment
i.e., π x r12 x h1 = πh2(r22 - r12)
`(22)/(7) xx 7^2 xx 21` = 1232h2
h2 = `(3234)/(1232)` = 2.625
= 2.625m
∴ Height of the embankment = 2.625m.
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