Question

A well with inside diameter 3 m is dug 14 m deep. Earth taken out of it is spread all around to a width of 4 m to form an embankment. Find the height of embankment.

Answer 1

Given:

Inside diameter of the well = 3 m

⇒ Radius of the well,

r = 1.5 m

Depth of the well,

h = 14m

Width of embankment = 4 m

Outer radius of embankment,

R = 1.5 + 4

= 5.5m

Let the height of embankment be H m.

Volume of earth dug out (well):

V1​ = πr²h

= π × (1.5)² × 14

= π × 2.25 × 14

= 31.5π m³

Volume of earth used to form embankment (hollow cylinder):

V2 ​= πH(R² − r²)

= πH (5.5)² − (1.5)²

= πH(30.25 − 2.25) = 28πH

Since volume of earth dug out = volume of embankment:

31.5π = 28πH    ...[π = π Cancel π]

H = `31.5/28`

= 1.125 m