Question

A well of diameter $4m$ is dug $21m$ deep. the earth taken out of its has been spread evenly all around it in the shape of a circular ring of width $3m$ to form an embankment. Find the height of the embankment.

Answer 1

Step 1: Find the volume of the well dug.

Given that, Diameter $=4m$

Radius $=2m$

Height $=21m$

The volume of soil dug from the well $={\mathrm{\pi r}}^2\mathrm{h}$

$$\begin{gathered} =\pi \times 2\times 2\times 21 \\ =84\pi \end{gathered}$$

Step 2: Find the height of the embankment.

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

$$\begin{gathered} \Rightarrow 84\pi =\pi \times \left(5^2-2^2\right)\times h \\ \therefore h=\frac{84}{25-4} \\ h=\frac{84}{21} \\ h=4m \end{gathered}$$

Hence, the height of the embankment is $4m.$