a well of diameter 3 m and 14m deep is dug. the earth taken out of it has been evenly spread all around it in the shape of a circular ring of width 4m to from an embankment. find the height of the embankment
Answers
Answer:
Depth of the cylindrical well,
h
1
=
14
m
Radius of the cylindrical well,
r
=
3
2
m
=
1.5
m
Width of embankment
=
20
m
Inner radius of the embankment,
r
=
3
2
m
Outer radius of the embankment, R
=
Inner radius
+
Width
R
=
1.5
m
+
4
m
=
5.5
m
Let the height of embankment be
h
Volume of the cylindrical well
=
Volume of the hollow cylindrical embankment
π
r
2
h
1
=
π
R
2
h
−
π
r
2
h
π
r
2
h
1
=
π
h
(
R
2
−
r
2
)
r
2
h
1
=
h
(
R
−
r
)
(
R
+
r
)
h
=
r
2
h
1
(
R
−
r
)
(
R
+
r
)
=
(
1.5
m
)
2
×
14
m
[
(
5.5
m
−
1.5
m
)
(
5.5
m
+
1.5
)
]
=
2.25
m
2
×
14
m
4
m
×
7
m
=
1.125
m
Therefore, the height of the embankment will be
1.125
m
.
Answer:
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