A well if diameter 7 m is dug 22.5 m deep. The earth taken out of it is spread around it at work of 10.5 m to form an embankment. Find the height of embankment.
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Answers
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Answer:
1.5 m
Step-by-step explanation:
(i) Volume of well:
Given:
Diameter = 7 m.
Then,radius = 3.5 m
Height = 12.5 m.
∴ Volume of well = πr²h
= π * (3.5)² * (22.5)
= 275.625π m³
(ii) Volume of Cylinder:
Given:
Width = 10.5 m
Internal radius = r₁ = 3.5 m.
Volume of cylinder with internal radius = πr₁²h
= πh(3.5)²
= 12.25πh
External radius = r₂ = 14 m
Volume of cylinder with external radius = πr₂²h
= πh(14)²
= 196πh
∴ Volume of cylinder = πh(196 - 12.25)
= πh(183.75)
= 183.75 πh m³
So, volume of embankment = 183.75 πh m³.
Now,
Volume of well = Volume of embankment
⇒ 275.625 π = 183.75 πh
⇒ 275.625/183.75 = h
⇒ h = 1.5 m
Therefore, height of the embankment = 1.5 m.
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