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A well of diameter $10 m$ is dug $14 m$ deep. The Earth taken out of it is spread evenly all around to a width of 5 $m$ to form an embankment. What is the height of the embankment?

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5.66m

3.33m

4.66m

answer is C.

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Detailed Solution

Given that a well of diameter

10 m

14 m

deep and width of embankment is 5

m

We have the following formulae,
Volume of a cylinder =

π r 2 h

Volume of a hollow cylinder =

π (R 2 − r 2) h

Volume of the well will be,

227 × 5 × 5 × 14 = 1100 m 3

We take R as the radius of the well and the embankment.
R = 5 + 5
=10m
Volume of earth dug = Volume of well
Then, the height of the embankment will be,

227 (102 − 52) h = 1100 227 (100 − 25) h = 1100 227 × 75 × h = 1100 h = 1100 × 7 22 × 75 h = 35075 = 4.66 m

Thus, the height of the embankment is 4.66m.
Therefore the correct option is 3.

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