Question

A well with $10m$ inside diameter is dug $8.4m$ deep. Earth taken out of it is spread all around it to a width of $7.5m$ to form an embankment. Find the height of the embankment.

Answer 1

Diameter of the well $=10m$



$\therefore$ Radius (r) = $\frac{10}{2}$$=5m$
Depth (h) $=8.4m$
$\therefore$ Volume of earth dug out = $\pi r^{2}h$
=$\frac{22}{7}\times 5\times 5\times 8.4m^3=660m^3$
Width of embankment$=7.5m$
$\therefore$ Outer radius$\left(R\right)=5+7.5=12.5m$
Area of embankment = $\pi (R^2-r^2)$
= $\frac{22}{7}\left[\right(12.5{)}^2-5^2]$
= $\frac{22}{7}(12.5+5)(12.5-5)$
= $\frac{22}{7}\times 17.5\times 7.5m^2=412.5m^2$
Let $h$ be the height of embankment, then
Volume of embankment $=412.5h=660$
$\Rightarrow h=\frac{660}{412.5}m$
$\Rightarrow$ $h=1.6019m\approx 1.6m$