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

Step 1: Calculate the volume of water flowing in 30 minutes

First, we need to determine the length of the water column that flows out of the canal in 30 minutes. We convert the time to hours (30 minutes = 0.5 hours) and multiply it by the speed of the water. Then, we calculate the volume of this water by multiplying its length, the given width of the canal, and its depth.

Step 2: Calculate the volume of water

Multiplying the length (5000 m), width (6 m), and depth (1.5 m) of the water column gives us the total volume of water that flows out of the canal in 30 minutes.

Step 3: Convert standing water depth to meters

The required standing water depth is given in centimeters, so we convert it to meters to maintain consistent units throughout our calculations. There are 100 centimeters in 1 meter.

Step 4: Calculate the irrigated area

The volume of water available for irrigation is equal to the area irrigated multiplied by the required standing water depth. We can rearrange this formula to find the irrigated area by dividing the total volume of water by the standing water depth.

Step 5: Final calculation of irrigated area

Performing the division, we find that the canal can irrigate an area of 562,500 square meters in 30 minutes.

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