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

Find the height of the embankment

Depth $\left(h_1\right)$ of well $=14m$
The radius $\left(r_1\right)$ of the circular end of the well $=\frac{3}{2}m$

Width of embankment $=4m$
It can be observed that our embankment will be cylindrical having an outer radius, $\left(r_2\right)=4+\frac{3}{2}=\frac{11}{2}m$

Let the height of the embankment be $\left(h_2\right)$

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

$$\begin{gathered} \pi \times {r_1}^2\times h_1=\pi \times ({r_2}^2-{r_1}^2)\times h_2 \\ \pi \times {\left(\frac{3}{2}\right)}^2\times 14=\pi \times \left[{\left(\frac{11}{2}\right)}^2–{\left(\frac{3}{2}\right)}^2\right]\times h_2 \\ \therefore h_2=\frac{9}{8} \\ =1.125m \end{gathered}$$

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