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

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answer is B.

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Detailed Solution

We will calculate the volume of cylinder of diameter

3 m

and height

14 m

.
Radius of cylinder

= 12 (Diameter)

⇒ radius= 12 (3) ⇒ radius=1 .5

From above we see that the radius of the cylinder is 1.5 m and height is 14m.
Volume of cylinder is given as:

V = π r 1 2 h

Substituting values or

r 1

and

h

in above formulas we have:

V = 227 × 1.5 2 × 14 ​ ⇒ V = 22 × 2.25 × 7 ​ ⇒ V = 154 × 2.25 ​ ⇒ V = 346.5

Therefore, the volume of the cylinder or we can say volume of soil dug is equal to

346.5 m 3

Let 'H' be the height of the embankment formed by excavating the soil around the cylinder formed by excavating the soil.
Therefore, the volume of the hollow cylinder formed is given as

V ‘ = π r 2 2 − r 1 2 × H

r 2 = radius of hollow cylinder = r 1 +width of hollow cylinder

r 2 = 1.5 + 4 = 5.5 m r 1 = 1.5 m

Substituting values in above formula. We have

V ‘ = 227 × {(5.5) 2 − (1.5) 2} × H ⇒ V ‘ = 227 × (30.25 − 2.25) × H ⇒ V ‘ = 227 × 28 × H ⇒ V ‘ = 22 × 4 × H ⇒ V ‘ = 88 H

So we see from above that the volume of the created hollow cylinder or embankment is

.
Since then, we know that the soil dug up from the cylinders is spread everywhere. The volume of the created embankment will therefore be equal to the volume of excavated soil.