Question

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

A well of diameter 3 m is dug 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

The shape of the well will be cylindrical.

Depth (h₁) of well = 14 m

Radius (r₁) of the circular end of well = 3/2 m

Width of embankment = 4 m

From the figure, it can be observed that our embankment will be in a cylindrical shape having outer radius (r₂) as 4 + 3/2 =11/2 m and inner radius (r₁) as 3/2 m

Let the height of embankment be h₂.

Volume of soil dug from well = Volume of earth used to form embankment

`pixxr_1^2xxh_1 = pixx(r_2^2-r_1^2)xxh_2`

`pixx(3/2)^2xx 14 =pixx[(11/2)^2-(3/2)^2]xxh`

`9/4xx14 = 112/4 xx h`

h = 9/8 = 1.125 m

Therefore, the height of the embankment will be 1.125 m.