Question

A well with $14m$ diameter is dug $8m$ deep. The earth taken out of it has been evenly spread all around it to a width of $21m$ to form embankment. Find the height of the embankment.

Answer 1

Given:
A well with $14m$ diameter is dug $8m$ deep and Width of the embarkment is $21m$.

Let, the inner radius be $r$, outer radius be $R$ and height be $h$.

$\therefore r=\frac{14}{2}=7m$ and $R=(7+21)=28m$

Volume of the earth taken out
$=\pi r^{2}h$

$=(\frac{22}{7}\times 7^2\times 8)m^3$

$=1232m^3$

Base area of embarkment
$=\pi (R^2-r^2)$

$=\frac{22}{7}(28-7)(28+7)$

$=2310m^2$

Now, height of the embarkment
$=\frac{Volumeoftheearth}{Baseareaofembarkment}$

$=\frac{1232}{2310}=0.533m=53.3cm$

Hence, the height of the embarkment is 53.3 cm.