# A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m

182 views

closed

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

+1 vote
by (30.3k points)
selected by

Let the height of the embankment be ‘h’ m

Radius of well = 4 m

Height of the well = 14 m

Volume of earth dug out (volume of cylinder) = πr2h

$\frac{22}7\times{4}\times{4}\times{14}$ m3

= 704 m3

Outer Radius of the embankment(R) = 4 m + 3 m = 7 m

Inner radius of the embankment(r) = 4 m

Volume of embankment = Volume of earth dug out

Volume of embankment = πR2h - πr2h

= πh (R2 – r2

= πh (72 – 42 )

= 33 πh

Volume of embankment = Volume of earth dug out

⇒ 33 πh = 704

⇒ h = $\frac{{704}\times{7}}{{33}\times{22}}$

⇒ h = 6.78 m