Question

A well of diameter $7m$ and $30m$ deep is dug and the soil obtained by digging the well is evenly spread out to form a platform of size $30m\times 10m$. Find the height of the platform.

Answer 1

For the cylindrical well diameter is $7m$ and depth is $30m$
Here $r=\frac{d}{2}=\frac{7}{2}$ and height $=30m$
For the cubical platform, length $l=30m$, breadth $=10m$ and height $=X$ $m$
volume of soil obtained by digging the well $=$ volume of soil used to prepare the platform.
$\Rightarrow \pi r^{2}h=l\times b\times h$
$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 30=30\times 10\times X$
$X=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{30}{30\times 10}$
$X=3.85m$
Hence height of the platform $=3.85m$