Question

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

Answer 1

Answer:

The height of the Embankment is 6.78 m

Step-by-step explanation:

Given :  

Inner radius of the well , r = 4 m

Depth of the well , H =   14 m

Volume of the well ( cylinder) = πr²×h

Embankment forms a hollow cylinder.

Width of the embankment = 3 m

Outer Radius of the  embankment, R = ( r + width) = (4 + 3) m = 7 m

Here, the earth obtained from digging the well of cylindrical shape is used to make a Embankment. So the volume of Earth will be equal to the volume of cylindrical well and it will be equal to volume of Embankment.

Let h be the height of the embankment.

Volume of the well ( cylinder) = Volume of the hollow cylinder(embankment)

πr²×H = π(R² - r²)×h

r²×H  = (R² - r²)×h

4² × 14 = (7² - 4²)h  

16 × 14 = (49 - 16)h

16 × 14 = 33h

h = (16 × 14)/33

h = 224/33

h = 6.78 m

Hence, The height of the Embankment is 6.78 m.

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Answer 2

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