Question

A well of inner diameter 14m 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 (ID)
D = 14 m
$A=\pi r^2$
$r=\frac{D}{2}=\frac{14}{2}=7m$
$A=\pi \left(7^2\right)=153.938m^2$
Volume of well
V = Ah
h = 12 m
V = (153.938)(12) = 1,847.256 $m^3$
Outside diameter (OD) of embankment
D + 7 + 7 = 14 + 7 + 7 = 28 m
OD area
$A=\pi r^2$
$r=\frac{D}{2}=\frac{28}{2}=14m$
$A=\pi (14{)}^2=615.752m^2$
Cross-sectional area of embankment
OD area - ID area = 615.752 $m^2$ - 153.938 $m^2$ = 461.814 $m^2$
Volume of well ALSO volume of embankment
V = (153.938)(12) = 1,847.256 $m^3$
$h=\frac{V}{A}=\frac{1,847.256m^3}{461.814m^2}=4m$
Height of embankment