# A well with 10 m inside diameter is dug 8.4 m deep.

Question:

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.

Solution:

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.