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A well is dug (from outside) 20 m deep and it has a diameter of 7 m. The earth which is so dug out is spread out on a rectangular plot $22 m$ long and $14 m$ broad. What is the height of the platform so formed?

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1.3m

2.5m

8.4m

4.3m

answer is B.

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Detailed Solution

It is given a well of diameter 7 m, depth 20 m and rectangular plot of length 22 m and breadth 14 m.
Since,
Radius =

D i a m e t e r 2

⇒

Radius (r) =

72 m

Volume =

π r 2 h

⇒ V o l u m e = 227 × 722 × 20

⇒ V o l u m e = 227 × 72 × 72 × 20

⇒ V o l u m e = 770 m 3

Now, length of the plot (l) = 22m
Breadth (b) =14m
Since, Volume of rectangular platform = Volume of the earth that dugout.
So, Volume of rectangular platform=770

m 3

Since, volume of rectangle =

l × b × h

So, Height =

V o l u m e l × b

⇒

Height =

770 22 × 14

⇒ H e i g h t = 52 m

⇒

Height =2.5

m

Therefore, the height of the platform is 2.5

m

.
Hence option (2) is correct.

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