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A well with $10 m$ inside diameter is dug $8.4 m$ deep. Earth taken out of it is spread all around it to a width of $7.5 m$ to form an embankment. Find the height of the embankment.

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1.6m

2.8m

4.3m

3.2m

answer is A.

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Detailed Solution

It is given a well of diameter 10 m, depth 8.4 m and width of embankment is 7.5 m.
Question Image

Since, radius =

D i a m e t e r 2

So, radius (r) is,

r = 102 ⇒ r = 5 m

Volume =

π r 2 h

⇒ V o l u m e = 227 × 52 × 8.4

⇒ V o l u m e = 227 × 5 × 5 × 8.4

⇒ V o l u m e = 660 m 3

Now,
Width of the embankment

= 7.5

m
Inner radius = Radius of a cylindrical well = 5 m
Outer radius = Width of embankment + Radius of cylindrical well
Outer radius = 7.5 m + 5 m
Outer radius =12.5 m
Since, Area of the material contained in a hollow cylindrical shell

= π R 2 − r 2

So, Area of the embankment =

π R 2 − r 2

⇒ A r e a o f t h e e m b a n k m e n t = 227 12.5 2 − 52

⇒

Area of the embankment =412.5

m 2

Volume of the embankment = Area of the embankment

\times

height of the embankment

= π R 2 − r 2 h

Volume of embankment = Volume of the earth that dugout = 660

m 3

So, Height of embankment =

V o l u m e o f e m b a n k m e n t A r e a o f e m b a n k m e n t

⇒ H e i g h t o f e m b a n k m e n t = 660 412.5 ⇒ H e i g h t o f e m b a n k m e n t = 1.60 m

Therefore, the height of the embankment is 1.6 m.
Hence option (1) is correct.

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