A well with inside diameter 10 m 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.
Question:

A well with inside diameter 10 m 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:

Inner radius of the well, $r=\frac{10}{2}=5 \mathrm{~m}$

Depth of the well, h = 8.4 m

Suppose the outer radius of the embankment is R m.

Width of the embankment = 7.5 m

∴ R − r = 7.5 m

⇒ R = 7.5 + 5 = 12.5 m

Let the height of the embankment be H m.

Now,

Volume of earth used to form the embankment = Volume of earth dugged out of the well

$\therefore \pi\left(R^{2}-r^{2}\right) H=\pi r^{2} h$

$\Rightarrow H=\frac{5^{2} \times 8.4}{(12.5)^{2}-(7.5)^{2}}$

$\Rightarrow H=\frac{210}{100}$

$\Rightarrow H=2.1 \mathrm{~m}$

Thus, the height of the embankment is 2.1 m.

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