Question

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

Answer 1

We have,

Diameter of well = 14 m

Radius of well = d/2 = 14/2 = 7m

Depth of well = 8 m

Volume of earth dug out from well = πr²h

= 22/7 × 7 × 7 × 8

= 1232 m³

This earth is spread out on width of 21 m.

Area × h = 1232

π(R² – r²) h = 1232

π(28² – 7²) h = 1232

22/7 (735) h = 1232

h = 1232×7 / 22×735

= 8624/16170

= 0.533 m

= 53.3 cm

∴ Height of embankment is 53.3 cm