Question

Urgent

A well of inner diameter 14m is dug to a depth of 12m .Earth taken out of it has been evenly spread all around it to a word of 7m to form an embankment.Find the height of the embankment so formed

Answer 1

(i) Volume of well:

Given Diameter = 14 m.

Radius = 7 m

height = 12 m.

We know that volume of cylinder = πr^2h

⇒ π * (7)^2 * 12

⇒ 588π.

(ii) Volume of embankment:

Given diameter of well = 14 m.

Given width = 7 m.

⇒ Internal radius r₁= 7 m.

⇒ Volume of internal radius = πr₁^2h

                                               = πh(7)^2

⇒ External radius r₂ = 7 + 7 = 14 m

Volume of external radius = πr₂^2h

                                           = πh(14)^2.

Volume of cylinder = πh(14)^2 - πh(7)^2

                                = πh(196 - 49)

                                = πh(147).

So, Volume of embankment = πh(147).

Now,

Volume of well = volume of embankment

⇒ 588π = πh(147)

⇒ h = 588/147

⇒ h = 4.

Therefore, the height of the embankment = 4 m.

Hope it helps!