Question

How many cubic metres of earth must be dug out to sink a well which is $20m$ deep and has a diameter of $7$ metres? If the earth so dug out is spread over a rectangular plot $28m$ by $11m$, what is the height of the platform so formed?

Answer 1

Diameter $=7m$
Radius $=3.5m$
​Depth $=20m$
​Volume of the earth dug out $=\pi r^{2}h$
$=\frac{22}{7}\times 3.5\times 3.5\times 20$
$=770m^3$
Volume of the earth piled upon the given plot = Volume of earth dug out
$\Rightarrow \text{length}\times \text{breadth}\times \text{height}=770m^3$
$\Rightarrow 28\times 11\times h=770m^3$
$\Rightarrow h=\frac{770}{28\times 11}$
$\therefore h=2.5m$
Therefore, height of the platform will be $2.5m$.