Answer

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Hint : Find the length of land the water covers in 40 minutes then calculate volume

We know width of canal = 5.4 m

And depth of canal = $1.8\,m$

It is given in the question that in \[60{\text{ }}min.\], \[25\,km\] of water flows through it.

So, in \[40{\text{ }}min\], The water will flow through the length,

\[\dfrac{{25}}{{60}}\, \times 40 = \dfrac{{50}}{3}\,km\]

$\dfrac{{50}}{3}\,km$ will be available for irrigation.

Hence, the volume of water in the canal = volume of land irrigated.

Volume of canal\[\; = l \times b \times h\]

\[ = 5.4 \times 1.8 \times \frac{{50000}}{3}\,{m^3}\]

Area of land irrigated if \[10\,cm\] standing water is required

\[ = 5.4 \times 1.8 \times \frac{{50000}}{3}\, \times \dfrac{1}{{0.1}}\,{m^2}\]

\[ = 16,20,000\,{m^2}\]

Hence the answer is \[16,20,000\,{m^2}\].

Note :- In this question we have calculated the volume of water that gets filled in 40 minutes then it is said that land is irrigated if there is 10 cm standing water. So we have divided the volume by 10 to get the required area of land that gets irrigated in 40 minutes.

We know width of canal = 5.4 m

And depth of canal = $1.8\,m$

It is given in the question that in \[60{\text{ }}min.\], \[25\,km\] of water flows through it.

So, in \[40{\text{ }}min\], The water will flow through the length,

\[\dfrac{{25}}{{60}}\, \times 40 = \dfrac{{50}}{3}\,km\]

$\dfrac{{50}}{3}\,km$ will be available for irrigation.

Hence, the volume of water in the canal = volume of land irrigated.

Volume of canal\[\; = l \times b \times h\]

\[ = 5.4 \times 1.8 \times \frac{{50000}}{3}\,{m^3}\]

Area of land irrigated if \[10\,cm\] standing water is required

\[ = 5.4 \times 1.8 \times \frac{{50000}}{3}\, \times \dfrac{1}{{0.1}}\,{m^2}\]

\[ = 16,20,000\,{m^2}\]

Hence the answer is \[16,20,000\,{m^2}\].

Note :- In this question we have calculated the volume of water that gets filled in 40 minutes then it is said that land is irrigated if there is 10 cm standing water. So we have divided the volume by 10 to get the required area of land that gets irrigated in 40 minutes.

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