Q. 184.0( 38 Votes )

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.

Hint. Required height =


Answer :

Given that,

Inner diameter = 14 cm


Therefore,


Radius = 7 cm


Also, Depth = 12 m


Therefore,


Volume of earth dug out = Πr2h


=


= 1848 m3


It is also given that,


Width of embankment = 7 m


Therefore,


Total radius = 7 + 7 = 14 m


Volume of embankment = Total volume – Inner volume


= Πro2h – Πr12h


= Πh (ro2 – r12)


= h (142 - 72)


= h (196 – 49)


= × 147


= 21 × 22h


= 462 × h m3


Since,


Volume of embankment = Volume of earth dug out


Therefore,


1848 = 462 h


h =


h = 4 m


Therefore,


Height of the embankment = 4 m

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