Question

A river of width $6m$ and height $1.5m$ flows with a speed of $10km/h$. It’s water is used to irrigate a field of area $‘a^{\prime }$ $m^2$. The field is said to be irrigated if the field is filled with water up to a height of $0.8m$. If it takes $30$ minutes to irrigate the field, find the value of $‘a^{\prime }$.

Answer 1

Solution:
A figure is drawn below to visualize the canal according to the given question.

From the figure, it can be seen that the shape of the cross-section of the canal is cuboidal. So, the volume of the water, flowing at the speed of $10km/h$ for $30$ minutes will be the same as the volume of water needed to irrigate the area with $0.8m$ of standing water.
To find the volume of water we need to find the length of the water flowing through the canal in $30$ minutes at the speed of $10km/h$.
We have,
Width of the canal$=6m$
Depth/height of the canal$=1.5m$
Speed of water flowing in a canal$=10km$/$h$.
Length of canal in 1hour$=10km$
Length of canal in $30$ minutes$=\frac{10\times 30}{60}=5km=5000m.$
Therefore,
Volume of canal$=l\times b\times h=5000\times 1.5\times 6m^3.$
Now,
Volume of water in canal$=$ Volume of area to be irrigated.
$=5000\times 1.5\times 6m^3=Areairrigated\times height$.
$=45000=Areairrigated\times 0.8$
$Areairrigated=\frac{45000}{0.8}=\frac{450000}{8}=56250m^2$.
Therfore, the value of $a$ is $56250$.