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A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

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1.125 m

1.26 m

1.57 m

1.28 m

answer is A.

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Detailed Solution

Given,
Depth or height of well

h_{1} = 14 m

Also, the radius

(r_{1})

of the circular end of well

= \frac{3}{2} m

Embankment width

= 4 m

The outer radius of embankment

(r_{2}) = 4 + \frac{3}{2}

r_{2} = \frac{11}{2} m

Suppose height of embankment =

h_{2} .

Here,
Soil dug from well volume = Earth volume to make embankment

π \times r_{1}^{2} \times h_{1} = π \times (r_{2}^{2} - r_{1}^{2}) \times h_{2}

π \times {(\frac{3}{2})}^{2} \times 14 = π \times [{(\frac{11}{2})}^{2} - {(\frac{3}{2})}^{2} \times h_{2}]

\frac{9}{4} \times 14 = \frac{112}{4} \times h_{2}

h_{2} = \frac{9}{8} = 1.125 m

Thus, height of embankment = 1.125 m.
Correct option is 1.

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