A well of diameter 3m is dug 14m deep. The earth taken oit of it has been spread evenly all around it the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment
Answers
Answer:
Height of the well = 14 m
Diameter of the well = 3 m
So, Radius of the well = 3/2 m
Volume of the earth taken out of the well = πr²h
= 22/7*(3/2)²*14
= 99 cu m
Outer radius of the embankment = R = (3/2 + 4)m = 11/2 m
Area of embankment = outer area - inner area
⇒ = πR² - πr²
= 22/7*[(11/2)² - (3/2)²]
= 22/7*[(121/4) - (9/4)]
= 22/7 × 112/4
= 88 m²
Height of the embankment = Volume/Area
= 99/88
Height of the embankment = 1.125 m
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