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Q.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

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a

1.5 m

b

1.6 m

c

1 m

d

1.125 m

answer is D.

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Detailed Solution

Given-
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment.
The shape of the well will be cylindrical as given below.
Question Image

Question Image

Given, depth

h 1

of well = 14 m
Diameter (d) of the circular end of the well =3 m
Radius,

r = d 2

⇒ r = 32 m

Width of the embankment = 4 m
From the figure, it can be said that the embankment will be a cylinder having an outer radius (

r 2

) as

4 + 32 = 112 m

and inner radius as

32 m

.
Now, let the height of the embankment be

h 2

.
Volume of soil dug from well = Volume of earth used to form embankment
Question Image

Question Image

So, the height of the embankment is 1.125 m.
So, the correct option is 4.

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