Question

A $20m$ deep well with diameter $7m$ is dug and the earth from digging is evenly spread out to form a platform $22m$ by $14m$. Find the height of the platform.

Answer 1

We have
Volume of the earth taken out of the well = volume of a cylinder of radius $\frac{7}{2}m$ and height $20m$

$=\pi \times r^2\times h$

$\Rightarrow$ $\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 20m^3=770m^3$

Let the height raised of $22m\times 14m$ platform be equal to $h$ meters.

Then, the volume of the earth in platform = volume of the earth taken out of the well

$22\times 14\times h=770$

$\Rightarrow h=\frac{770}{22\times 14}m\Rightarrow h=\frac{5}{2}m=2.5m$

$\therefore$ Height of the platform$=2.5m$