Question

A well is dug $20m$ deep and it has a diameter of $7m$. The earth which is so dug out is spread out on a rectangular plot $22m$ long and $14m$ broad, what is the height of the platform so formed?

Answer 1

Diameter of the well $=7m$
$\Rightarrow$ Radius $\left(r\right)=\frac{7}{2}m$
Depth $\left(h\right)=20m$
Volume of earth dug out $=\pi r^{2}h$
$=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 20m^3$

$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 20$

$=770m^3$
Length of plot $\left(l\right)=22m$
and breadth $\left(b\right)=14m$
Let $h$ be the height of the platform of earth
Then ,

Volume of rectangular plot $=$ Volume of earth dug out

$\Rightarrow lbh=\text{Volume of earth dug out}$

$\Rightarrow h=\frac{\text{Volume of earth dug out}}{l\times b}$

$\Rightarrow h=\frac{770m^3}{22m\times 14m}$

$\Rightarrow h=\frac{5}{2}m$

$\Rightarrow h=2.5m$

Therefore, Height of the platform $=2.5m$.