Question

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

Answer 1

Let h be the required height of the embankment.
The shape of the embankment will be like the shape of a cylinder of internal radius 1 m
and external radius (5 + 1) m = 6 m.
The volume of the embankment will be equal to the volume of the earth dug out from the well. Now, the volume of the earth dug out = volume of the cylindrical well
= π × 1² × 14 m³ = 14 π m³
Also, the volume of the embankment = π(6² – 1²) h cm³ = 35 π h m³



Hence, we have
35πh m³= 14π m³
h = $\frac{14}{35}$ = 0.4
Hence, the required height of the embankment = 0.4 m.