A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an ambankment. Find the height of the embankment.
Answers
Given : Diameter of the well = 10 m
Inner radius of the well , r = 10/2 m = 5 m
Depth of the well , H = 8.4 m
Volume of the well (cylinder) = πr²×h
Embankment forms a hollow cylinder.
Width of the embankment = 7.5 m
Outer Radius of the embankment, R = ( r + width) = (5 + 7.5) m
R = 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
(5)² × 8.4 = [ (12.5) ² - (5)²]h
25 × 8.4 = [156.25 - 25]h
25 × 8.4 = 131.25 h
h = (25 × 8.4)/131.25
h = 8.4 /5.25
h = 1.6 m
Hence, the height of the Embankment is 1.6 m .
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Answer:
Step-by-step explanation:
πr²×H = π(R² - r²) × h
r² × H = (R² - r²)× h
(5)² × 8.4 = [ (12.5) ² - (5)²]h
25 × 8.4 = [156.25 - 25]h
25 × 8.4 = 131.25 h
h = (25 × 8.4)/131.25
h = 8.4 /5.25
h = 1.6 m