A well of diameter 3m is dug 14m deep. the earth taken out of its has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment Find the height of embankment...............
Answers
Answer:
1.125 m
Step-by-step explanation:
let the diameter of the well of cylindrical shape is. d= 3m ,
r(cy)= 3/2 = 1.5 m
h(cy)= 14m
The earth taken out spread around it in the form of ring whose width is 4m , then the outer of the ring is r(0) =. (4+1.5)=5.5m
volume of well = volume of embankment
πrsquare h = π(Rsquare - rsquare) h
3/2 (3/2)(14) = (5.5) square - (1.5) square h
63/2 = 28 h
63/2(28) =h
h= 63/56
h= 1.125m
Step-by-step explanation:
Height of the well = 14 m.
Diameter of the well = 3m.
Therefore, Radius of the well = 3/2 m.
According to question now :
Volume of the earth taken out of the well = πr²h
=> 22/7 × 3/2 × 3/2 × 14
=> 22 × (3/2)² × 2
=> 44 × 9/4
=> 11 × 9
=> 99 cm.
Outer radius of embankment (R) = (3/2 +4)
=> 11/2 m
Now,
Area of embankment = outer area - inner area
=> πR² - πr²
=> 22/7 [(11/2)² - (3/2)²]
=> 22/7 × 112/4
=> 88 m²
Height of the embankment = Volume / Area
=> 99/88
=> 1.125 m
Therefore, the height of the embankment is 1.125 m