Question

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

Answer 1

Diameter of a well = 14 m

$\therefore Radius\left(r\right)=\frac{14}{2}$ = 7 m

Depth (h) = 8 m

$\therefore$ Volume of the earth dugout = $\pi r^2$ h

= $\frac{22}{7}\times 7\times 7\times 8m^3=1232m^3$

Width of embankment = 21 m

$\therefore$ Outer radius = 21 + 7 = 28 m

$\therefore$ Area of embankment = $\pi (R^2-r^2)$

=$\frac{22}{7}(R+r)(R-r)=\frac{22}{7}\times (28+7)(28-7)m^3$

=$\frac{22}{7}\times 35\times 21=2310m^2$

$\therefore$ Height of the embankment =$\frac{\text{Volume of earth}}{\text{Area of embankment}}$

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