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 in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Diameter of the well = d = 3 m

$\Rightarrow$ Radius of well $=r=\frac{d}{2}=1.5m$

Height of the well = h= 14 m

Volume of earth dug out = volume of well
$=\pi .r^2.h=\pi \times 1.5\times 1.5\times 14=31.5\pi m^3$

Let the height of the embankment be $h_{1}m$

Volume of embankment
$=\pi .\left(\right(r_2{)}^2-\left(r_1{)}^2\right)).h_1$ $(r_2=5.5,r_1=1.5)$
$=\pi .\left(\right(5.5{)}^2-\left(1.5{)}^2\right)).h_1=\pi .(30.25-2.25).h_1=28\pi .h_1{m}^3$

According to the given condition , we have:

Volume of Earth Dug out = volume of embankment

$\Rightarrow 31.5\pi =28\pi .h_1$

$h_1=\frac{31.5}{28}=1.125m$