A well with inner radius $ 4 \mathrm{~m} $ is dug $ 14 \mathrm{~m} $ deep. Earth taken out of it has been spread evenly all around a width of $ 3 \mathrm{~m} $ it to form an embankment. Find the height of the embankment.

Given:

A well with inner radius \( 4 \mathrm{~m} \) is dug \( 14 \mathrm{~m} \) deep.

Earth taken out of it has been spread evenly all around a width of \( 3 \mathrm{~m} \) it to form an embankment.

To do:

We have to find the height of the embankment.

Solution:

Inner radius of the well $r=4 \mathrm{~m}$

Depth of the well $h=14 \mathrm{~m}$

This implies,

Volume of the earth dug out $=\pi r^{2} h$

$=\frac{22}{7} \times 4 \times 4 \times 14$

$=704 \mathrm{~m}^{3}$
Width of the embankment $w=3 \mathrm{~m}$

This implies,

Outer radius $\mathrm{R}=4+3$

$=7 \mathrm{~m}$
Let $h$ be the height of the embankment.

Therefore,

$\pi(\mathrm{R}^{2}-r^{2}) h=704$

$\Rightarrow \frac{22}{7}[7^{2}-4^{2}] h=704$

$\Rightarrow \frac{22}{7}[49-16] h=704$

$\Rightarrow \frac{22}{7} \times 33 h=704$

$\Rightarrow h=\frac{704 \times 7}{22 \times 33}$

$\Rightarrow h=\frac{32 \times 7}{33}$

$\Rightarrow h=\frac{224}{33}$

$\Rightarrow h=6.78$

The height of the embankment is $6.78 \mathrm{~m}$. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

18 Views

Kickstart Your Career

Get certified by completing the course

Get Started