Question

a well of 11.2m diameter is dug 8m deep.the earth taken out has been spread all around it to a width of 7m to form a circular embankment.find the height of embankment

Answer 1

so we know well is cylinder
    

radius = 11.2 /2 = 5.6 m
height = 8 m 
so volume of earth dig
   
πr²h
= 22/7 × 5.4² × 8
= 787.76 m³

so spreading will create a hollow cylinder
 
let the height be  h
so 
formula for volume of hollow sphere is 
πh(r₂²-r₁²)
787.76 = πh(12.4²-5.6²)
h=787.76/π(12.4²-5.6²)
h = 1.97 m

Answer 2

Diameter of well = 11.2m
radius(r) = 5.6m
depth (h) = 8m
The earth taken out = The volume of the well = V
V = πr²h = π×5.6²×8 m³

As the volume of earth taken has been used to make the embankment, the volume of embankment is the same as volume of well.
A circular embankment is a hollow cylinder with some width
In this case  width(w) = 7m.
The inner radius of embankment(r1) = 5.6m (same as the well)
       outer radius of embankment(r2) = (r1+w) = (5.6+7)m = 12.6m
Let the height = h1 m

Volume of embankment = volume of well
⇒π×h1×[(r2)² - (r1)²] = πr²h
⇒ π×h1×[(r2)² - (r1)²] = π×5.6²×8
⇒ h1×[12.6² - 5.6²] = 5.6²×8
⇒ h1 = (5.6²×8) / (12.6²-5.6²)
⇒ h1 = 1.97m

Height of embankment is 1.97m