Question

A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.

Answer 1

Depth $\left(h_1\right)$ of the well = 14 m
Radius $\left(r_1\right)$ of the circular end of the well $=\frac{4}{2}m=2m$
Height $\left(h_2\right)$ of embankment = 4o cm = 0.4 m
Let the width of embankment be x.
From the figure, it can be observed that the embankment will be cylindrical in shape having outer radius $\left(r_2\right)$ as (2 + x)m and inner radius $\left(r_1\right)$ as 2m.
Volume of earth dug from the well = Volume of earth used to form embankment
$\pi r_1^2{h}_1-\pi (r_2^2-r_1^2)h_2$
$\pi (2{)}^{2}14=\pi ((2+x{)}^2-2^2)$
$x^2+4x-40=0$
$x=10m$
Therefore, the width of the embankment will be 10m.