Question

Water in a canal, $30$ dm wide and $12$ dm deep, is flowing with a speed of $10km/hr$. How much area will it irrigate in $30$ minutes, if $8$ cm of standing water is required for irrigation

• A. $225000m^2$
• B. $25000m^2$
• C. $22000m^2$
• D. $2250m^2$

Answer 1

The correct option is A $225000m^2$

Given,
The width of the canal=$30$dm=$300$cm=$3$m
Depth of the canal=$12$dm=$120$cm=$1.2$m
Given,
Water flowing with velocity of $10$km per hour.
Length of the water column formed in $\frac{1}{2}$hour
=$\frac{1}{2}\times 10$
=$5$km
=$5000$m
Hence,
The volume of the water flowing in $\frac{1}{2}$hour
=Volume of cuboid of length of $5000$m width $3$m and depth $1.2$m
=$5000\times 3\times 1.2$
=$18000m^3$
Let A $m^2$ be the area irrigated in $\frac{1}{2}$hour then,
$A\times 8cm=18000m^3$
$=>A\times \frac{8}{100}m=18000m^3$
$=>A=225000m^2$
Hence, the required area is $225000m^2$