Question

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

Answer 1

The shape of the well will be cylindrical.
Depth (h₁) of well = 21m
Diameter of the well = 14m
Radius (r₂) of well = 14m
Width of embankment (r₂)
= 7m + 14m
= 21m
Let height of the embankment be h₂
Volume of earth spread on the embankment
= πh2(r₂² - r₁²)
= rh₂(r₂ + r₁)(r₂ - r₁)

= `(22)/(7) xx "h"_2 xx 28 xx 14`
= 1232h₂
Volume of soil dug from well = Volume of earth used to form embankment
i.e., π x r₁² x h₁ = πh₂(r₂² - r₁²)

`(22)/(7) xx 7^2 xx 21` = 1232h₂

h₂ = `(3234)/(1232)` = 2.625
= 2.625m
∴ Height of the embankment = 2.625m.