Question

A well with 10 m inside diameter is dug 14 m deep. earth taken out of it is spread all around to a width of 5 m to form an embankment .find the height of embankment.

Answer 1

Given: Diameter of the well (d) $=10m$

$\Rightarrow$ Radius of well (r) $=\frac{d}{2}=\frac{10}{2}=5m$

And, Depth of well (h) $=14m$

Volume of earth dug out $=\pi r^{2}h$

$=\pi \times 5^2\times 14$

$=350\pi m^3$

Now, Let the height of embankment be $\text{H}m$.

So, Volume of embankment $=350\pi m^3$

$\Rightarrow \pi (r+5{)}^2\text{H}-\pi r^2\text{H}=350\pi$

$\Rightarrow \text{H}\left[\right(r+5{)}^2-r^2]=350$

$\Rightarrow \text{H}\left[\right(5+5{)}^2-5^2]=350$

$\Rightarrow \text{H}(100-25)=350$

$\Rightarrow \text{H}=\frac{350}{75}$

$\Rightarrow \text{H}=4.67$

Hence, the height of the embankment is $4.67m$.