Math, asked by rohitgaike, 11 months ago

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

Answered by bhagyashreechowdhury
2

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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Answered by tyagimadhvi5
1

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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