A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Answers
Given : Diameter of the well = 14 m
Inner radius of the well , r = 14/2 m = 7 m
Depth of the well , H = 8 m
Volume of the well (cylinder) = πr²×h
Embankment forms a hollow cylinder.
Width of the embankment = 21 m
Outer Radius of the embankment, R = ( r + width) = (7 + 21) m
R = 28 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
(7)² × 8 = [ (28) ² - (7)²]h
49 × 8 = (28 + 7) (28 - 7) h
[a² - b² = (a + b) (a - b)]
49 × 8 = 35 × 21 × h
h = (49 × 8)/35 × 21
h = (7 × 8)/5 × 21
h = 8 /15 m
h = 8/15 × 100
h = 800/15
h = 53.3 cm
Hence, the height of the Embankment is 53.3 cm .
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Answer:
Step-by-step explanation:
πr²×H = π(R² - r²) × h
r² × H = (R² - r²)× h
(7)² × 8 = [ (28) ² - (7)²]h
49 × 8 = (28 + 7) (28 - 7) h
[a² - b² = (a + b) (a - b)]
49 × 8 = 35 × 21 × h
h = (49 × 8)/35 × 21
h = (7 × 8)/5 × 21
h = 8 /15 m
h = 8/15 × 100
h = 800/15
h = 53.3 cm