a well of diameter 3 m is dug 14 m deep . The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment . find the height of the embankment.
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a well of diameter 3 m is dug 14 m deep . The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment . find the height of the embankment.
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Answer:
Step-by-step explanation:
Diameter =3m
Radius=3/2m
Height=14m
Well is in the form of cylinder. If earth is taken out of to form a embankment
Hence,
Volume of cylinderical well=volume of embankment
Width of embankment=4m
Total radius =4+3/2 m=11/2m
Volume of cylinder=volume of embankment
πr²H=π(R²-r²)h
3/2×3/2×14=(11/2+3/2)(11/2-3/2)h
[a²-b²=(a+b)(a-b)]
3/2×3/2×14=14/2×8/2×h
By solving it
h=9/8m
Answer:
1.125 m
Step-by-step explanation:
Volume of well = Volume of Embankment
(3/2)² * 14 = (11/2 + 3/2)(11/2 - 3/2)h
9/4 * 14 = 14/2 * 8/2 * h
9/2 * 7 = 7 * 4 * h
(9/2) / 4 = h
h=9/2 * 1/4
h= 1.125 m
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