A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it a width of 7 m to form an embankment. Find the height of embankment so formed.


Given: 

Inner diameter of well = 14 m

Depth of well = 12 m

To find: Here we have to find the height of embankment so formed.

Solution:

Given that the earth removed to dug the well is used to form an embankment. So, the volume of earth removed to dug well is equal to the volume of earth used to form an embankment. We can use this to calculate the height of the embankment.



Now,


Dimensions of well:

Diameter (d) = 14 m

So,

Radius (r) = 7 m

Height (h) = 12 m

Volume of earth dug out = πr2h  

Volume of earth dug out = $\frac{22}{7} \ \times \ 7\ \times \ 7\ \times \ 12$  

Volume of earth dug out = 1848 m3  

Dimensions of embankment:

Outer Diameter (D) = Diameter of well $+$ 2(Width of earth around the well)

Outer Diameter (D) = 14 $+$ 2(7) m

Outer Diameter (D) = 28 m

So,

Outer Radius (R) = 14 m

Inner Radius (r) = 7 m

Volume of embankment = π(R $-$ r)2H  

Volume of embankment = $\frac{22}{7} \ \times \ \left( 14^{2} \ -\ 7^{2}\right) \ \times \ h$

Volume of embankment = $\frac{22}{7} \ \times \ ( 14 \ -\ 7) \ \times \ ( 14 \ +\ 7) \ \times \ h$

Volume of embankment = $\frac{22}{7} \ \times \ 7\ \times \ 21\ \times \ h$

Volume of embankment = 462 $\times$ h 

Volume of earth removed to dug well is equal to the volume of earth used to form an embankment. So,

Volume of embankment = Volume of earth dug out

462 $\times$ h = 1848

h = $\frac{1848}{462}$

h = 4 m



Therefore, the height of embankment is 4 m.

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Updated on: 10-Oct-2022

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