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

Ans:

### STEP BY STEP SOLUTION

Let’s draw a diagram for this question to understand it better:

The earth (sand) need to be taken out from the well and same to be used in the ring outside.

Step 1: We will calculate the earth (sand) taken our from the well.

Since the volume of the cylinder, V = π r2 h

Given that the diameter of the cylinder (well) = 3 m

Therefore, the radius of the cylinder (well) =

The height of the cylinder (Depth of the well) = 14 m

Volume of the earth =

=

=

= 11 x 9 = 99 m3

Step 2: Next, we will calculate volume of the earth used to make the embankment around the well.

Since, this embankment is in shape of a cylinder with internal and external diameters

the differential area of the circular ring = π (R22  – R12 )

Internal diameter, D1 of the ring = 3m

External diameter, D2 of the ring = 3m + 2 x 4m = 11m

the differential area of the circular ring =

=  = 88 m2

Now if the height of the embankment is H,

then the volume of the embankment = Area x height = 88 H m3

Step 3: We will calculate the height of the circular ring around the well (embankment).

Since the earth taken out from the well is being used to make the embankment

Hence the volume of the earth taken out from the well = Volume of the earth used to make the embankment

∴ 99 = 88 H

∴ 9 = 8 H

∴ H =  = 1.125 m

Therefore, the height of the embankment is 1.1.25 m

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