**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 r^{2} 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 m^{3}

**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 (R

_{2}^{2}_{ } – R

_{1}^{2 })

Internal diameter, D_{1} of the ring = 3m

internal radius, R

_{1} =

External diameter, D_{2} of the ring = 3m + 2 x 4m = 11m

external radius, R

_{2} =

the differential area of the circular ring =

=

= 88 m

^{2}

Now if the height of the embankment is H,

then the volume of the embankment = Area x height = 88 H m^{3}

**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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