Question

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

Answer 1

Given,

Diameter of the well = 3 m

So, the radius of the well = 3/2 m = 1.5 m

Depth of the well (h) = 14 m

Width of the embankment (thickness) = 4 m

So, the radius of the outer surface of the embankment = (4 + 1.5) m = 5.5 m

Let the height of the embankment be taken as h m

We know that the embankment is a hollow cylinder

Volume of the embankment = π (R² – r²) × h

= π (5.5² – 1.5²) × h            ….. (i)

Volume of earth dug out = π × r² × h

= π × 2² × 14    ….. (ii)

On equating both (i) and (ii) we get,

π (5.5² – 1.5²) × h = π × (3/2)² × 14

(30.25 – 2.25) x h = 9 x 14/ 4

h = 9 x 14/ (4 x 28)

h = 9/8 m

Therefore, the height of the embankment is 9/8 m.