Question

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment. Find the height of the embankment.

Answer 1

Height of the well = 14 m
Diameter of the well = 3 m
So, Radius of the well = $\frac{3}{2}$ m
Volume of the earth taken out of the well $=\pi r^{2}h=\frac{22}{7}\times (\frac{3}{2}{)}^2\times 14=99m^3$

Outer radius of the embankment = R = ($\frac{3}{2}$ + 4)m = $\frac{11}{2}$ m
Area of embankment = outer area - inner area
⇒

$=\pi R^2-\pi r^2$

$=\frac{22}{7}\left[\right(\frac{11}{2}{)}^2-\left(\frac{3}{2}{)}^2\right]$

$=\frac{22}{7}[\frac{121}{4}-\frac{9}{4}]$

$=\frac{22}{7}\times \frac{112}{4}=88m^2$
Height of the embankment =$\frac{Volume}{Area}=\frac{99}{88}=1.125m$
Height of the embankment = 1.125 m