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 = Πr^{2}h

=

= 1848 m^{3}

It is also given that,

Width of embankment = 7 m

Therefore,

Total radius = 7 + 7 = 14 m

Volume of embankment = Total volume – Inner volume

= Πr_{o}^{2}h – Πr_{1}^{2}h

= Πh (r_{o}^{2} – r_{1}^{2})

= h (14^{2} - 7^{2})

= h (196 – 49)

= × 147

= 21 × 22h

= 462 × h m^{3}

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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