Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

AcademicMathematicsNCERTClass 10

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 needed $=8\ cm$.

To do: 

We have to find the irrigated area.

Solution:

A canal is in the shape of a 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,

The volume of water in canal $=$ Volume of area irrigated

The 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 $= 562500\ m^{2}$

The irrigated area in 30 minutes is $562500\ m^{2}$.

raja
Updated on 10-Oct-2022 13:25:34

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