Water in a canal, $6\ m$ wide and $1.5\ m$ deep, is flowing with a speed of $10 \ km/hour$. How much area will it irrigate in $30$ minutes; if $8\ cm$ standing water is needed?
Given: Width of the canal $= 6\ m$ ,Depth of the canal $=1.5\ m$, speed of
water flow$=10\ km/h$, time given$=30\ minutes=\frac{1}{2} hr$ , standing water $=8\ cm$.
To do: To find the irrigated area.
Solution:
Canal is in the shape of cuboid , where,
Breadth $=6\ m$
Height $=1.5\ m$
Speed of canal $=10\ km/hr$
Length of canal in 1 hour $=10\ km$
Length of canal in 60 minutes $=10\ km$
Length of canal in 1 minute $=\frac{1}{60}\times10\ km$
Length of canal in 30 minute $=\frac{30}{60}\times10=5\ km=5000\ m$
Now,
Volume of canal $= length\times breadth\times height$
$= 5000\times6\times1.5\ m^{3}$
Now,
Volume of water in canal $=$ Volume of area irrigated
Volume of water in canal $=$ Area irrigated $\times$ Height
$\Rightarrow 5000\times6\times1.5 = Area\ irrigated \times\frac{8}{100}$
Area irrigated $=\frac{5000\times6\times1.5\times100}{8}$
Area irrigated $= 562500\ m^{2}$
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