A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

#### Solution

Given data is as follows:

r = 7m

h = 8 m

R - r = 21 m

We have to find the height of the embankment.

Let the height of the embankment be H meter.

From the given data we have,

Volume of earth in embankment = Volume of earth dug out

Volume of embankment = `pi (R^2 - r^2)H`

Volume of earth dug out = `pir^2h`

Therefore, we have

`pi(R^2 - r^2) H = pir^2 h`

` (R^2 - r^2) H = r^2h`

`(R-r)(R+r)H=r^2h`

Here,

R - r = 21m

But,

r = 7 m

Therefore,

R - 7 = 21

R = 28 m

Substituting the values in the above equation, we have

`(28-7)(28+7)H=7xx7xx8`

`21xx35xxH = 7xx7xx8`

`H = 8/15 m`

= 0.533 m

= 53.3 cm

Therefore the height of the embankment is equal to 53.3 cm