In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
Answers
Step-by-step explanation:
Radius of well, R = 10/2 = 5 m,
Depth of the well, H = 14 m
Width of the embankment = 5 m,
the outer radius of the embankment, r = R+5 = 5 +5 = 10 m
the inner radius of the embankment R = 5 m
Height of the embankment = H
volume of the embankment = volume of the well
[πr² – πR²]H = πr²h
π [r² – R²] H = πr²h
[r² – R²] H = r²h
[10² – 5²] H = 5² * 14
H = [5² * 14] / [100 – 25]
H= 14/3 m
∴ the height of the embankment H is 14/3 m
This is your answer
a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
answer:
Given: diameter of the well (d) = 10 m
R
a
d
i
u
s
o
f
t
h
e
w
e
l
l
(
l
)
=
d
2
=
10
2
=
5
m
and Depth of well (h) = 14 m
V
o
l
u
m
e
o
f
e
a
r
t
h
d
u
g
o
u
t
=
π
×
r
2
×
h
=
π
×
5
2
×
14
m
3
=
350
π
m
3
Let the height of embankment be H m.
N
o
w
v
o
l
u
m
e
o
f
e
m
b
a
n
k
m
e
n
t
=
350
π
×
m
3
⇒
π
(
r
+
5
)
2
×
H
–
π
×
r
2
H
=
350
×
p
i
⇒
H
×
[
(
5
+
5
)
2
–
5
2
]
=
350
⇒ H (100 – 25) = 350
⇒ H =
350
75
=
14
3
=
4.66
Hence the height of the embankment is 4.66 m.
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embakment, the height of the embankment is ________.
Medium
Solution
verified
Verified by Toppr
Correct option is C)
Well with 10m diameter is dug 14m deep.
⇒ Cylindrical radius =
2
10
=5m
Volume =πr
2
h
=
7
22
×5×5×14
=1100 cubic meter
Is taken out and spread width of 5m.
( diagram )
⇒R
1
=5+5=10m
r=5m
⇒V=π(R
2
−r
2
)h
1100=
7
22
(10
2
−5
2
)h
350=(100−25)h
h=
75
350
=
3
14
⇒h=4.66m
Hence, the answer is 4.66m.