Question

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

• A. $220500m^2$
• B. $22500m^2$
• C. $220000m^2$
• D. $225000m^2$

Answer 1

The correct option is D $225000m^2$

Given,
Width of the canal=$30$dm=$300cm$=$3m$
Depth of the canal=$12dm$=$120cm$=$1.2m$
Water is flowing with a speed of $10$ km/hour.
$\therefore$ length of water column formed in$\frac{1}{2}$hour
=$\frac{1}{2}\times 10$km
=$5$km
=$5000m$
Hence Volume of water column formed in$\frac{1}{2}$hour
=Volume of cuboid of length $5000m$,width $3m$ and depth $1.2m$
=$5000\times 3\times 1.2m^3$
=$18000m^3$
Let A$m^2$ be the area irrigated in$\frac{1}{2}$hour then,
$a\times 8=18000m^3$
$a\times \frac{8}{100}m18000m^3$
$a=225000m^2$
Hence the canal irrigates $225000m^2$area in$\frac{1}{2}$hour