Question

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

Answer 1

Given :

Well diameter $\left(d\right)=3m,$ height $\left(h\right)=14m$

Embankment width $=4m$

Volume of well $=$ Volume of embankment

$\Rightarrow \pi r^{2}h=\pi R^{2}H\Rightarrow r^{2}h=R^{2}H\Rightarrow {\left(1.5\right)}^2\times 14=({5.5}^2-{1.5}^2)\times H$

$\Rightarrow 3.15=284\Rightarrow H=\frac{31.5}{28}=1.125m$

Height of embankment $=1.125m$