A well with $14\ m$ diameter is dug $8\ m$ deep. The earth taken out of it has been evenly spread all around it to a width of $21\ m$ to form an embankment. Find the height of the embankment.

 Given:

A well with $14\ m$ diameter is dug $8\ m$ deep. The earth taken out of it has been evenly spread all around it to a width of $21\ m$ to form an embankment.

To do:

We have to find the height of the embankment.

Solution:

Diameter of the well $= 14\ m$

This implies,

Radius $(r) = 7\ m$

Depth of the well $(h) = 8\ m$

Therefore,

Volume of the earth dugout $= \pi r^2h$

$=\frac{22}{7} \times 7 \times 7 \times 8$

$=1232 \mathrm{~m}^{3}$

Width of embankment $=21 \mathrm{~m}$

This implies,

Outer radius $=21+7$

$=28 \mathrm{~m}$

Area of the embankment $=\pi(\mathrm{R}^{2}-r^{2})$

$=\frac{22}{7}(\mathrm{R}+r)(\mathrm{R}-r)$

$=\frac{22}{7} \times(28+7)(28-7)$

$=\frac{22}{7} \times 35 \times 21$

$=2310 \mathrm{~m}^{2}$

The height of the embankment $=\frac{\text { Volume of earth }}{\text { Area of embankment }}$

$=\frac{1232}{2310}$

$=0.533 \mathrm{~m}$

$=53.3 \mathrm{~cm}$

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Updated on: 10-Oct-2022

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