Question

A well of diameter 14 metre is dug 15 M deep the earth taken out of it has been spread evenly all around it in the shape of a circular linked with 7 m to form an embankment find the height of the embankment​

Answer 1

Solution :-

Both well and the embankment are in the shape of cylinder.

Since the mud is evenly spread all around the well to form the embankment, then the volume of well = volume of embankment

Volume of well = πr²h

Diameter = 14 m

then radius = 14/2 = 7 m

Height = 15 m

⇒ π*7*7*15 

⇒ Volume of well = 735 π m³

Volume of the embankment -

The embankment is in the shape of a hollow cylinder.

It inner diameter =  14 m

So, Radius r = 14/2 = 7 m

Its outer radius R = inner radius + width

⇒ 7 + 7 = 14 m

Volume of inner part of the cylinder = πr²h

⇒ π(7)²*h

= 49 πh m³

Volume of the outer part of the cylinder = πR²h

⇒ π(14)²*h

⇒ 196 πh m³

Volume of embankment = Volume of outer part - Volume of inner part

⇒ 196 πh m³ - 49 πh m³

Volume of embankment = 147 πh m³

Now,

Volume of well = Volume of embankment

735 π m³ = 147 πh m³

⇒ h = 735/147

⇒ h = 5

So, the height of the embankment is 5 m

Answer

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