A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Given data is as follows:
Inner diameter of the well = 10 m
Height = 8.4 m
Width of embankment = 7.5 m
We have to find the height of the embankment.
Given is the diameter of the well which is 10 m. Therefore,
r = 5 m
The outer radius of the embankment,
R = Inner radius of the well + width of the embankment
= 5 + 7.5
= 12.5 m
Let H be the height of the embankment.
The volume of earth dug out is equal to the volume of the embankment. Therefore,
Volume of embankment = Volume of earth dug out
$\pi\left(R^{2}-r^{2}\right) H=\pi r^{2} h$
$22 / 7 \times\left(12.5^{2}-5^{2}\right) \mathrm{H}=22 / 7 \times 5 \times 5 \times 8.4$
H = 1.6 m
Thus, height of the embankment is 1.6 m.