A well of diameter 3m dug 14m deep . The earth taken out of it has been spread evenly all around it in the shape of circular ring of width 4m to form an embankment . Find the height of embankment.
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Answers
Answer:
The shape of the well will be cylindrical as shown in the figure below:
Given:
Depth (h
1
) of well = 14 m
Radius (r
1
) of the circular end of well =
2
3
m
Width of embankment = 4 m
From the figure, it can be observed that our embankment will be in a cylindrical shape having outer radius, (r
2
)=4+
2
3
=
2
11
m,
Let height of embankment be h
2
.
Volume of soil dug from well = Volume of earth used to form the embankment
π×r
1
2
×h
1
=π×(r
2
2
−r
1
2
)×h
2
⟹π×(
2
3
)
2
×14=π×[(
2
11
)
2
−(
2
3
)
2
×h
2
]
⟹
4
9
×14=
4
112
×h
2
⟹h
2
=
8
9
=1.125 m
So, the height of the embankment will be 1.125 m.
Step-by-step explanation:
Inner radius of embankment = 1.5m
Outer radius of embankment = 5.5 m
Volume of well = Volume of embankment
πr²h=π(R²-r²)H
1.5×1.5×14=(5.5+1.5) (5.5-1.5) H
1.5×1.5×14=7×4×H
H=2.25÷2
H= 1.125m
Height of embankment is 1.125m.