A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.
Answers
Answer:
Width of the embankment is 5 cm.
Step-by-step explanation:
Given :
The height of the deep well is in the form of a cylinder, H = 14 m
Diameter of well = 2 m
radius of well , r = 1 m
Volume of cylinder = πr²hH
= π × 1² × 14 = 14π m³
Volume of cylinder = 14π m³ ………(1)
The Embankment is in the form of cylindrical shell.
Height of embankment , h = 4 cm = 40/100 = 0.4 m
Let the width of the embankment be x
width of the embankment = R - r
Outer Radius of the embankment , R = (r + x) = (1 + x )
Inner Radius of the embankment , r = 1
Volume of embankment = π(R² - r²)h
= π( (1+ x)² - 1²)× 0.4
Volume of embankment = π (1² + x² + 2x - 1) 0.4 ……….(2)
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
Volume of the deep well (cylinder) = Volume of Embankment
14π = π (1² + x² + 2x - 1 ) 0.4
[From eq 1 & 2]
14/.4 = 1 + x² + 2x - 1
140/4 = x² + 2x
35 = x² + 2x
x² + 2x - 35 = 0
x² + 7x - 5x - 35 = 0
[By middle term splitting]
x(x + 7) - 5(x + 7) = 0
(x - 5) (x + 7) = 0
(x - 5) = 0 or (x + 7) = 0
x = 5 or x = - 7
Since, width can't be negative , so x ≠ - 7
Therefore, x = 5
Hence, width of the embankment is 5 cm.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
Solution:-
Diameter of well = 2 m
So, radius of well = 1 m
Height = 14 m
Dimensions of embankment =
h = 40 cm or 0.4 m
Radius = ?
Width of embankment = R - r
Volume of earth dug out = Volume of embankment
⇒ 22/7*1*1*14 = 22/7*(R² - 1)*0.4
⇒ 44 = 8.8(R² - 1)/7
⇒ = R² - 1 = (44*7)/8.8
⇒ R² - 1 = 35
⇒ R² = 35 + 1
⇒ R² = 36
⇒ R = 6 m
Now width of embankment = 6 - 1
= 5 m