A well having 10m inside diameter is dug 8.4m deep.earth is taken out and spread all around it to a width of 7m to form a beautiful embankment.find the height of the embankment
Answers
Answer:
The height of the Embankment is 1.6 m.
Step-by-step explanation:
Given :
Inner diameter of the well = 10 m
Inner radius of the well , r = 10/2 = 5 m
Depth of the well , H = 8.4 m
Embankment forms a hollow cylinder.
Width of the embankment = 7.5 m
Outer Radius of the embankment, R = ( r + width) = (5 + 7.5) m = 12.5 m
Here, the earth obtained from digging the well of cylindrical shape is used to make a Embankment. So the volume of Earth will be equal to the volume of cylindrical well and it will be equal to volume of Embankment.
Let h be the height of the embankment.
Volume of the well ( cylinder) = Volume of the hollow cylinder(embankment)
πr²× H = π(R² - r²)×h
r²× H = (R² - r²)×h
5² × 8.4 = (12.5² - 5²)h
25 × 8.4 = (156.25 - 25)h
25 × 8.4 = 131.25h
h = (25 × 8.4)/131.25
h = 8.4/ 5.25 = 1.6 m
h = 1.6 m
Hence, The height of the Embankment is 1.6 m.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
The volume of earth(soil) taken out which is equal to the volume of Cylinder.
Volume of earth taken out from well = Volume embankment
⇒πr
2
h=π(R
2
2
−R
1
2
)×H
⇒5
2
×8.4=((12.5)
2
−5
2
)×H
⇒H=
131.25
25×8.4
=1.6m