Question

A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment ?

Answer 1

Let r and h be the radius and depth of the well, respectively.

\[r = \frac{3}{2} m\] and h = 14 m

Let R and H be the outer radius and height of the embankment, respectively.

∴ R = r + 5 =\[\frac{3}{2}\] \[\frac{13}{2}\] m

Now,
Volume of the earth used to form the embankment = Volume of the earth dug out of the well

\[\pi\left( R^2 - r^2 \right)H = \pi r^2 h\]
\[ \Rightarrow H = \frac{r^2 h}{R^2 - r^2}\]
\[ \Rightarrow H = \frac{\left( \frac{3}{2} \right)^2 \times 14}{\left( \frac{13}{2} \right)^2 - \left( \frac{3}{2} \right)^2} = \frac{63}{80} = 0 . 79 m \left( Approx \right)\]

Thus, the height of the embankment is approximately 0.79 m.