a well of inner diameter 14m is dug to a depth of 12m . Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment . Find the height of the embarkment so formed
Answers
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•volume of well or earth dug out = πr^2h
diameter = 14m , radius =14/2=7m
depth / height = 15m
•now volume = 22/7×(7)^2×15
=105×22
•volume of embankment =π(R^2-r^2)×h
outer radius (R) = outer width + inner radius
= 7+7=14m
inner radius(r) = 7 m
height = ?
•volume = 22/7 ( 14^2-7^2)×h
=22/7×196-49×h
=22/7×147×h
=22×21×h
•earth taken out of well is spread over all around it forming a embankment
•volume of well = volume of embankment
105×22=21×22×h
105×22/21×22 = h
105×22/462=h
h=5m
hence height is 5 m
hope helped
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Answer:
4m
Step-by-step explanation:
(i) Volume of well:
Diameter = 14 m.
Then radius = 7 m.
Height = 12 m.
Volume of cylinder = πr²h
= (22/7) * (7)² * 12
= 1848 m³
(ii) Volume of embankment:
Inner diameter = 14 m.
Internal radius r₁ = 7 m
External radius = r₂ = 14 m.
Now,
∴Volume of cylinder with internal radius = πr₁²h
= π(7)²h
∴ Volume of cylinder with external radius = πr₂²h
= π(14)²h
∴ Volume of cylinder = πh[14² - 7²]
= πh[196 - 49]
= 147πhm³
= 147(22/7)h
= 462 m³
So, volume of embankment = 462m³.
Now,
Volume of well = volume of embankment
⇒ 1848 = 462h
⇒ h = 4 m.
Therefore, Height of the embankment = 4 m.
Hope it helps!