Question

well of diameter 4m is dug 21 m deep the earth taken out of it has been spread evenly all around it in the shape of circular ring of width 3 m to form an embankment.find the height of the embankment

Answer 1

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Answer 2

Given : Well of diameter 4m is dug 21 m deep the earth taken out of it has been spread evenly all around it in the shape of circular ring of width 3 m to form an embankment.

To find : The height of the embankment.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the height of the embankment)

Radius of the well = Diameter ÷ 2 = (4 ÷ 2) metres = 2 metres

First of all, we have to calculate the volume of earth taken out during the formation of the well.

So, the volume of earth (that has been taken out) :

= π × (radius of the well)² × depth of the well

= (22/7) × (2)² × 21

= 264 m³

Now,

The volume of the embankment = The volume of earth (that has been taken out) = 132 m³

The outer radius of the embankment = Radius of the well + Width of the embankment = (2 + 3) cm = 5 cm

The inner radius of the embankment = Radius of the well = 2 cm

Let, the height of the embankment = h metres

So,

The volume of the embankment :

= π × [(Outer radius)² - (Inner radius)²] × height of the embankment

= π × [(5)² - (2)²] × h

= (22/7) × (25 -4) × h

= (22/7) × (21) × h

= 66h m³

Now, comparing the two values of the volume of the embankment, we get :

66h = 264

h = 264/66

h = 4

So, the height of the embankment = h metres = 4 metres

(This will be considered as the final result.)

Hence, the height of the embankment is 4 metres.