a well of radius 7m is dug to a depth of 12m. earth taken out it has been evenly spread all around to form a circular ambankment of width 7m. find the height of the embankment
Answers
The height of the embankment is 4 m.
Step-by-step explanation:
The dimension of the cylindrical well:
Radius, r = 7 m
Height, h = 12 m
We know that,
The volume of the earth dug out is given by,
= Volume of the cylinder
= π r² h
= 22/7 × 7 × 7 × 12
= 1848 m³
The dimension of the circular embankment:
Width, w = 7 m
So, its inner radius, r = 7 m
And
Outer radius, R = 7 + 7 = 14 m
Let the height of the embankment be "h" m
∴ The volume of the embankment is given by,
= [Outer Volume] – [Inner Volume]
= πR²h - πr²h
= 22/7 * h * [14² – 7²]
= [21 * 22] * h
= (462*h) m³
Now,
We know that,
[Volume of the earth dug out] = [Volume of the embankment]
⇒ 1848 = 462*h
⇒ h = 1848/462
⇒ h = 4 m ← height of the embankment
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The height of the embankment is 4 m.
Step-by-step explanation:
The dimension of the cylindrical well:
Radius, r = 7 m
Height, h = 12 m
We know that,
The volume of the earth dug out is given by,
= Volume of the cylinder
= π r² h
= 22/7 × 7 × 7 × 12
= 1848 m³
The dimension of the circular embankment:
Width, w = 7 m
So, its inner radius, r = 7 m
And
Outer radius, R = 7 + 7 = 14 m
Let the height of the embankment be "h" m
∴ The volume of the embankment is given by,
= [Outer Volume] – [Inner Volume]
= πR²h - πr²h
= 22/7 * h * [14² – 7²]
= [21 * 22] * h
= (462*h) m³
Now,
We know that,
[Volume of the earth dug out] = [Volume of the embankment]
⇒ 1848 = 462*h
⇒ h = 1848/462
⇒ h = 4 m ← height of the embankment
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