Question

A well of diameter 14 m. is dug 15 m. deep. The earth taken out of it has been spread evenly to form circular embankment of width 7 m. Find the height of the embankment.



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Answer 1

Answer:

5 m

Step-by-step explanation:

Diameter of well = 14 m.

Let the height of embankment be 'h' m.

Radius of earth or soil taken out = 7 m.

Height of soil taken out = 15 m.

Then, radius of well with embankment = 7 + 7 = 14 m.

∴ π * (14² - 7²) * h = π * 7² * 15

⇒ h = (7² * 15)/(14² - 7²)

      = 735/147

      = 5 m.

Therefore, height of the embankment = 5 m.

Hope it helps!

Answer 2

Step-by-step explanation:

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