A well with 14m diameter is dug 8m deep. The earth taken out of it has been evenly spread all around it to a width of 21m to form an embankment. Find the height of the embankment.
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Solution
Diameter of the well =14m
∴ Radius(r) =142=7m Depth of well (h) =8m ∴ Volume of earth dug out = πr2h =227×7×7×8m3=1232m3 Width of embankment =21m ∴ outer radius =21+7=28m ∴ Area of embankment = π(R2−r2) =227(282−72)m2=227(28+7)(28−7)m2=227×35×21m2=2310m2 Let h be the height of embankment, then Volume of embankment = 2310×h. ∴2310h=1232 h=12322310=0.53m=53cm Hence height of embankment= 53cm