A well of diameter 3 m is dug 14 m deep. The earth taken out of it is 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 1.125 m .
Step-by-step explanation:
SOLUTION :
Given :
Diameter of the well = 3 m
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 1.125 m .
HOPE THIS ANSWER WILL HELP YOU….
SOLUTION___☺✌
Given,_ Radius of well, r=3/2
Height, h= 14m
Therefore, the volume of the earth taken out of the well
=πr^2h
=22/7×3/2×3/2×14
= 99m^3
Outer radius of embankment=R=(3/2+4)m= 11/2m
Area of embankment= outer area- inner area
= πR^2- πr^2
= 22/7×[(11/2)^2-(3/2)^2]
=22/7×[121/4-9/4]
=22/7×112/4
= 88m^2
Now, height of embankment,= Volume/Area
= 99/88= 1.125m Ans.
★【MARK BRAINLIEST】
Follow me GUYS ☺☺