Question

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

Answer 1

Given, diameter $\left(d_1\right)=3m\Rightarrow radius\left(r_1\right)=1.5$

diameter $\left(d_2\right)=14m$ $\Rightarrow radius\left(r_2\right)=5.5$

Volume of earth taken out $=$ Volume of embankment

$\Rightarrow \pi r^{2}h=\pi (r_2^2-r_1^2)\times H$

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

$\Rightarrow H=\frac{2.25\times 14}{28}=1.125m$

$\therefore$ Height of embankment $=1.125m$