Question

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

Answer 1

The shape of the well is considered to be cylindrical as shown in the figure.
Given:
Depth $\left(h\right)$ of well $=20$ m
Radius $\left(r\right)$ of circular end of well = $\frac{7}{2}m$
Area of platform = Length x Breadth $=22\times 14$m ${}^2$
Assume height of the platform $=Hm$
The volume of soil dug from the well will be equal to the volume of soil in platform.
Volume of soil from well = Volume of platform

$⟹\pi r^{2}h$ = Area of platform x Height of platform

$\pi \times (\frac{7}{2}{)}^2\times 20=22\times 14\times H$

$H=\frac{22}{7}\times \frac{49}{4}\times \frac{20}{22\times 14}$

$H=\frac{5}{2}=2.5m$

Hence, the height of such a platform will be $2.5m$ .