Question

A rectangular water tank of the base $11m\times 6m$ contains water up to a height of $5m$.

If the water in the tank is transferred to a cylindrical tank of radius $3.5m$, find the height of the water level in the tank.

Answer 1

Length of the cuboidal tank, $l=11m$

The breadth of the cuboidal tank, $b=6m$

Height of cuboidal tank, $h=5m$

Base radius of a cylindrical tank, $r=3.5m$

Find out

We have to determine the height of the water level in the tank

Solution

According to the given data

Length of the cuboidal tank, $l=11m$

The breadth of the cuboidal tank, $b=6m$

Height of cuboidal tank, $h=5m$

The volume of the tank $=lbh$

Volume of tank$=11\times 6\times 5=330m^3$

Water in a cylindrical tank

Volume of a cylinder $={\mathrm{\pi r}}^2\mathrm{h}$,

where $r$ is the base radius

$h$ is the height of the cylinder

The volume of water in the tank $=$volume of the cuboidal tank

The volume of water in a cylindrical tank $=\mathrm{\pi }{\left(3.5\right)}^2\mathrm{h}$

$$\begin{gathered} 330=\frac{22}{7}\times \left(3.5\right)\times \left(3.5\right)\times h \\ 330=38.5\times h \\ h=8.57m \end{gathered}$$

Therefore, the height of the cylindrical tank$=8.57m$