A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment. Find the height of the embankment.
Answers
Answer:
The height of the Embankment is 9/8 m or 1.125 m.
Step-by-step explanation:
Given :
Diameter of the well = 3
Inner radius of the well , r = 3/2 m
Depth of the well , H = 14 m
Volume of the well ( cylinder) = πr²×h
Embankment forms a hollow cylinder.
Width of the embankment = 4 m
Outer Radius of the embankment, R = ( r + width) = (3/2 + 4) m = (3 + 8)/2 = 11/2 m
R = 11/2 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
(3/2)² × 14 = [ (11/2) ² - (3/2)²]h
9/4 × 14 = [121/4 - 9/4]h
9/4 × 14 = [112/4]h
9 × 14 = 112h
h = (9 × 14)/112
h = 9/8 m = 1.125 m
Hence, The height of the Embankment is 9/8 m = 1.125 m .
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Answer:
The height of the Embankment is 9/8 m or 1.125 m.
Step-by-step explanation:
Given :
Diameter of the well = 3
Inner radius of the well , r = 3/2 m
Depth of the well , H = 14 m
Volume of the well ( cylinder) = πr²×h
Embankment forms a hollow cylinder.
Width of the embankment = 4 m
Outer Radius of the embankment, R = ( r + width) = (3/2 + 4) m = (3 + 8)/2 = 11/2 m
R = 11/2 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
(3/2)² × 14 = [ (11/2) ² - (3/2)²]h
9/4 × 14 = [121/4 - 9/4]h
9/4 × 14 = [112/4]h
9 × 14 = 112h
h = (9 × 14)/112
h = 9/8 m = 1.125 m
Hence, The height of the Embankment is 9/8 m = 1.125 m .