A well with inner diameter 14m is 15m deep and the earth taken out is spread all around to a width of 7m to form an embankment. Find the height of the embankment.

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10 m

9 m

5 m

7 m

answer is C.

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Detailed Solution

⇒ radius = diameter 2 ⇒ radius = 142 = 7

So, the radius of the well is 7m and height 15m.

We are also given that the excavated earth extends around the well to form an embankment.
So first we find out the volume of the removed earth.
Now consider the formula for the volume of a cylinder.

So using this we get the volume of earth excavated as,

⇒ Volume dug out = π × (7) 2 × 15 ⇒ Volume dug out = 227 × (7) 2 × 15 ⇒ Volume dug out = 22 × 7 × 15 ⇒ Volume dug out = 2310

So we get the volume of excavated earth as 2310 cubic meters.
We are given that the excavated soil is spread all around to a width of 7m to form an embankment.

So, because of the embankment the outer radius of the well is,

⇒ Outer radius = Inner Radius+Width of Embankment ⇒ Outer radius = 7 + 7 ⇒ Outer radius = 14 m

Area = π r 2

⇒ Area of embankment = π Outer Radius 2 − π Inner Radius 2

⇒ Area of embankment = π 142 − π 72 ⇒ Area of embankment = 196 π − 49 π ⇒ Area of embankment = 147 π

Since,

⇒ Area of embankment = 227 × 147 ⇒ Area of embankment = 22 × 21 ⇒ Area of embankment = 462

So we get a waterfront area of 462 m2.
Now we will find the volume of the embankment.
Now assume that the height of the embankment is

H

⇒ Volume of embankment = Area of embankment × Height ⇒ Volume of embankment = 462 × H ⇒ Volume of embankment = 462 H

Since the volume of excavated soil is used to create the embankment, the volume of the embankment is equal to the volume of excavated soil.
So let's compare the values from equations (1) and (2). Then we get