Question

A well with diameter 3 m is digout to the depth of 14 m. The earth digout is spreaded out 4 m round the well evenly in the form of circular ring to make a plateform. Find the height of the plateform.

Answer 1

Given:

∵ Diameter of well = 3 m

Radius of well (r) = \(\frac { 3 }{ 2 }\) m

And the depth (h) = 14 m

∴ The volume of the earth digout from the well

= πr² = \(\frac { 22 }{ 7 }\) × \(\frac { 3 }{ 2 }\) × \(\frac { 3 }{ 2 }\) × 14

= \(\frac { 22\times 3\times 3 }{ 2 }\) = 99 m³

∵ Since, radius of the well is \(\frac { 3 }{ 2 }\) m and a ring is formed round the well. The ring is 4 m broad.

∴ radius of the well with ring r₁ = \(\frac { 3 }{ 2 }\) + 4 = \(\frac { 11 }{ 2 }\) m

and the radius of the well r₂ = \(\frac { 3 }{ 2 }\) m

Let the height of the circular ring be h

Then the volume of the earth of plate form = 88 × h m³

Now volume of the earth of plate form = volume of earth digout.

88 × h = 99

∴ h = \(\frac { 99 }{ 8 }\) = \(\frac { 9 }{ 8 }\) = 1.125 m

Hence the height of plate form = 1.125 m.