Question

Earth dug out on digging a circular tank of diameter $17.5$ m is spread all around the tank uniformly to a width of 4 m to from an embankment of height $2$ m.Calculate the depth of the circular tank correct upto two decimal places .

Answer 1

Diameter of circular tank$=17.5$m

$\therefore$ Radius$=\frac{17.5}{2}$m$=8.75$m

Width of earth embankment$=4$m

Height$=2$m

Let it be the depth of the well then volume of earth taken out of

$\pi r^{2}h=\frac{22}{7}\times {\left(8.75\right)}^2\times h$

$=\frac{22}{7}\times \frac{875}{100}\times \frac{875}{100}h$

$=\frac{22}{7}\times \frac{35}{4}\times \frac{35}{4}h$ ....$\left(1\right)$

Volume of platform formed by earth taken out

$=\pi \{{\left(\frac{51}{4}\right)}^2-{\left(\frac{35}{4}\right)}^2\}\times 2$

$=2\times \frac{22}{7}\times \frac{(51-35)(51+35)}{16}$

$=2\times \frac{22}{7}\times \frac{16\times 86}{16}=\frac{3784}{7}$sq.m .........$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we have

$\frac{22}{7}\times \frac{35}{4}\times \frac{35}{4}h=\frac{3784}{7}$

$\Rightarrow h=2.246$m

$\therefore$Depth of the tank$=2.25$m up to $2$ decimal places