A well 20m in diameter is dug 14m deep and the earth taken out is spread all round it to a width of 5m to form an embankment. The height of the embankment is

# A well 20m in diameter is dug 14m deep and the earth taken out is spread all round it to a width of 5m to form an embankment. The height of the embankment is

1. A
10m
2. B
11m
3. C
11.2m
4. D
11.5m

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### Solution:

Option C) is the correct answer because,
Given:
Diameter of well = 20m
Then,
radius of well(r)= Diameter ÷ 2=10m
Height of well (h) = 14m
Width of embankment = 5m
The earth taken out is spread all around the well, therefore, the radius of embankment if taken from the centre will be R.
= r + 5R
= 10+5R
= 15m
Now, to find the height of the embankment we have to equate the volume of the well and the volume of the embankment.
Volume of well = Volume of embankment
πr²h=π(R²−r²)×Hπ(10)²×14
=π(152−102)×Hπ(10)²×14
=π(225−100)×Hπ(10)²×14
=π(125)×HH
=100×14125H
=565H
=11.2m
∴ The height of the embankment = 11.2m.

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