In a corner of a rectangular field with dimensions $35 \mathrm{~m} \times 22 \mathrm{~m}$, a well with $14 \mathrm{~m}$ inside diameter is dug $8 \mathrm{~m}$ deep. The earth dug out is spread evenly over the remaining part of the field. Find the rise in the level of the field.
We have,
Length of the fiel, $l=35 \mathrm{~m}$,
Width of the field, $b=22 \mathrm{~m}$,
Depth of the well, $H=8 \mathrm{~m}$ and
Radius of the well, $R=\frac{14}{2}=7 \mathrm{~m}$,
Let the rise in the level of the field be $h$.
Now,
Volume of the earth on remaining part of the field = Volume of earth dug out
$\Rightarrow$ Area of the remaining field $\times h=$ Volume of the well
$\Rightarrow$ (Area of the field - Area of base of the well) $\times h=\pi R^{2} H$
$\Rightarrow\left(l b-\pi R^{2}\right) \times h=\pi R^{2} H$
$\Rightarrow\left(35 \times 22-\frac{22}{7} \times 7 \times 7\right) \times h=\frac{22}{7} \times 7 \times 7 \times 8$
$\Rightarrow(770-154) \times h=1232$
$\Rightarrow 616 \times h=1232$
$\Rightarrow h=\frac{1232}{616}$
$\therefore h=2 \mathrm{~m}$
So, the rise in the level of the field is 2 m.