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:

Let r m be the radius and d m be the depth of the well that is dug.

Volume of the well = πr2d = π(5 m)2(8.4 m) = 660 m3

An embankment has the shape of hollow cylinder with thickness. Its inner radii is equal to the well's radii, i.e. r = 5 m, and its outer radii is R = (5 + 7.5 )= 12.5 cm.

Then, the volume of the embankment = πh(R − r2)

Volume of the well = Volume of the embankment

659.73 m3 = πh((12.5 m)2 − (5 m)2)​

$\mathrm{h}=\frac{660 \mathrm{~cm}^{3}}{\frac{22}{7} \times\left[(12.5 \mathrm{~m})^{2}-(5 \mathrm{~m})^{2}\right]}=1.6 \mathrm{~m}$

Hence, the height of the embankment is 1.6 m.

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