Question

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

• A. 2.0 m
• B. 3.87 m
• C. 2.95 m
• D. 1.125 m

Answer 1

The correct option is

D

1.125 m

The shape of the well is cylindrical

Depth ($h_1$) = 14m

Radius of the circular end of well($r_1$) = 1.5m

Width of embankment = 4m

From the figure, $r_2$ = 4 + 1.5 = 5.5m (Radius of inner circle + outer circle)

Let height of embankment dug be $h_2$

Volume of soil dug from well = Volume of embankment

$\pi {r_1}^2{h}_1=\pi ({r_2}^2-{r_1}^2)h_2$

$\pi \times (1.5{)}^2\times 14=\pi ((5.5{)}^2-(1.5{)}^2)h_2$

$\pi \times (1.5{)}^2\times 14=\pi (5.5-1.5\left)\right(5.5+1.5)h_2$
$\frac{\pi \times (1.5{)}^2\times 14}{\pi \times 4\times 7}=h_2$

Solving the above equations, $h_2$ = 1.125m