A well of diameter 3 m ad 14 m deep is dug.

Solution:

Given a well with diameter 3 m and height 14 m. The earth dug out from well is used to make a circular embankment of 4m width.

We have to find the height of the embankment.

Let R be the radius of well

Let H be the height of well

Let r be the radius of embankment

Let h be the height of embankment

$R=\frac{1}{2} \times$ diameter of well

$=\frac{1}{2} \times 3$

$=1.5 \mathrm{~m}$

$H=14 \mathrm{~m}$

Width of the circular embankment $=4 \mathrm{~m}$

Radius of the circular embankment $r=($ Width of embankment $+R) \mathrm{m}$

$=(4+1.5) \mathrm{m}$

$=5.5 \mathrm{~m}$

Volume of well (Earth Dug) $=\pi R^{2} H$

$=\pi \times\left[(1.5)^{2}\right] \times 14$

Volume of the circular embankment $=\pi r^{2} h$

$=\pi \times\left[(5.5)^{2}-(1.5)^{2}\right] \times h$

According to the question

Volume of the earth dug = Volume of the circular embankment

Therefore,

$\pi \times(1.5)^{2} \times 14=\pi \times\left[(5.5)^{2}-(1.5)^{2}\right] \times h$

$\frac{3}{2} \times \frac{3}{2} \times 14=[(5.5-1.5)(5.5+1.5)] \times h$

$\frac{9}{4} \times 14=4 \times 7 \times h$

$h=\frac{9 \times 14}{4 \times 4 \times 7}$

$h=\frac{9}{8} \mathrm{~m}$