Question

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

Answer 1

The shape of the well will be cylindrical as shown in the figure below:
Given:
Depth ($h_1$) of well = 14 m
Radius ($r_1$) of the circular end of well = $\frac{3}{2}$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, $\left(r_2\right)=4+\frac{3}{2}=\frac{11}{2}$ m,

Let height of embankment be $h_2$.

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

$\pi \times r_1^2\times h_1=\pi \times (r_2^2-r_1^2)\times h_2$

$⟹\pi \times {\left(\frac{3}{2}\right)}^2\times 14=\pi \times [{\left(\frac{11}{2}\right)}^2-{\left(\frac{3}{2}\right)}^2\times h_2]$

$⟹\frac{9}{4}\times 14=\frac{112}{4}\times h_2$

$⟹h_2=\frac{9}{8}=1.125$ m

So, the height of the embankment will be $1.125$ m.