Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Answer 1

Inner diameter of well =14 m

$\therefore$ Inner radius $=\frac{14}{2}=7m$

Depth (h)=12 m

$\therefore$ Volume of earth dig out $=\pi r^{2}h$

$=\frac{22}{7}\times (7{)}^2\times 12m^3$

$=\frac{22}{7}\times 7\times 7\times 12m^3=1848m^3$

Width of the embankment of the well =7 m

$\therefore$ Outer radius (R)=7+7=14 m.

Let height of the embankment =h

$\therefore$ Volume $=\pi R^{2}h-\pi r^{2}h$

$=\pi h(R^2-r^2)=\frac{22}{7}h(R^2-r^2)$

$\therefore \frac{22}{7}h({14}^2-7^2)=1848$

$\Rightarrow \frac{22}{7}(14+7)(14-7)=1848$

$\Rightarrow \frac{22}{7}h\times 21\times 7=1848$

$\Rightarrow 462h=1848$

$\therefore h=\frac{1848}{462}=4$

$\therefore$ Height of embankment =4 m