A well of diameter 3m is dug 14m   deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

# A well of diameter 3m is dug   deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

1. A
0.4875m
2. B
0.7875m
3. C
0.7888m
4. D
0.8875m

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### Solution:

Given that a well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment.
The formula for the volume of a cylinder of radius, r and height, h is given by  .
The formula for the volume of a hollow cylinder of inner radius, r, outer radius, R and height, h is  .
Let the height of the embankment be h.
Radius of the cylinder is   So, r = 1.5m
The radius of the well is 1.5 m.
⇒ Volume of well
⇒ Volume of well
The volume of well is  .
The outer radius, R of embankment = inner radius + width of embankment

The outer radius of the embankment is, R=5.5m.
⇒ Volume of embankment
⇒ Volume of embankment
⇒ Volume of embankment   The volume of the embankment is  .
Since,
Volume of the well = the volume of embankment

h = 0.7875 m
Thus, the height of the embankment is 0.7875m.
Therefore, the correct answer is option (2).

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