Question

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

Answer 1

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Answer 2

Answer:

The Height of the Embankment is 1.125 meters.

Step-by-step explanation:

Height of the well = 14 meter

Diameter of the well = 3 meter

Radius of the well = Diameter / 2 = 3/2 m

Volume of the earth taken out of the well = πr²h

= 22/7*(3/2)²*14

= 99 $m^{3}$

Outer radius of the embankment = R = (3/2 + 4)meter = 8 + 3/ 2 = 11/2 meter

Area of embankment = Outer Area - Inner Area

⇒ πR² - πr² (R is Bigger radius and r is smaller radius)

=> 22/7*[(11/2)² - (3/2)²]

=> 22/7*[(121/4) - (9/4)]

=> 22/7 × 112/4

=> 88 m²

Height of the embankment = Volume Of Earth Taken Out / Area Of Embankment

= 99/88

Height of the embankment = 1.125 m

Therefore, the height of the embankment is 1.125 meters.