Question

A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form an embankment. Find the height of embankment?

Answer 1

Hello mate!

Given radius of the well = 5 m 
Height of the well = 14 m 
Width of the embankment = 5 m 
Therefore radius of the embankment = 5 + 5 = 10 m 
Let h be the height of the embankment 
Hence the volume of the embankment = volume of the well  
That is π(R – r)2h = πr2h (102 – 52) x h 
= 52 x 14 (100 – 25) x h
= 25 x 14 h
= (25 x 14)/75
= 14/3 
Therefore, h = 4.67 cm (nearly)

hope this helps you out!

Answer 2

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Volume of a cylinder = V = pi x r^2 x h 

volume of earth taken out = 22/7 x 5 x 5 x 14 = 1100m^3 

Let the height of embankment be H 

volume of earth used 1100m^3 

When you make the embankment 

The volume of the of the outer cylinder - volume of the inner cylinder = volume of earth 

Outer radius is Inner radius + 5m width = 10m 

( pi x 10 x 10 x H ) - ( pi x 5 x 5 x H ) = 1100 

pix100xH - pix25xH = 1100 
pi x 75 x H = 1100 
H = 1100 / 75pi = 1100 x 7 
________ 
75 x 22 
= 4.666metres



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