Question

A well of diameter 3m is dug 14m deep. The earth taken out is spread evenly all around it in shape of a circular ring of width 4m to form an embankment. Find the height of embankment.

Answer 1

Answer:

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Answer:4.1

Given: Height of the well = 14 m

Diameter of the well = 3 m

To find: Height of embankment

Proof: Both well and embankment are in the form of cylinder

Let well be cylinder A and embankment be cylinder B

Since mud of well is distributed in embankment

⇒ Volume of Well = Volume of embankment

Firstly, we find the Volume of well:

Volume of the earth taken out of the well = πr2h

= 99 m3

So, Volume of well = 99m3

For Cylinder B

Outer radius = R = Inner radius + width

Volume of embankment = Volume of cylinder with outer Radius

– Volume of cylinder with inner radius

= πR2h – πr2h

= πh(R2 – r2)

= πh(R – r)(R + r)

= 22 × 4 × h

= 88h m2

Volume of Well = Volume of embankment

⇒ 99 = 88h

⇒ h = 1.125m

Height of the embankment = 1.125 m

HOPE IT HELPS

Answer 2

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$\mathfrak{The\:Answer\:is}$

Height of the well = 14 m

Diameter of the well = 3 m

So, Radius of the well = 3/2 m

Volume of the earth taken out of the well = πr²h

= 22/7*(3/2)²*14

= 99 cu m

Outer radius of the embankment = R = (3/2 + 4)m = 11/2 m

Area of embankment = outer area - inner area

⇒ = πR² - πr²

= 22/7*[(11/2)² - (3/2)²]

= 22/7*[(121/4) - (9/4)]

= 22/7 × 112/4

= 88 m²

Height of the embankment = Volume/Area

= 99/88

Height of the embankment = 1.125 m

$\boxed{Hope\:This\:Helps}$

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