Final answer:
In 20 minutes, 90 million liters of water flows out of the lake, as calculated by multiplying the flow rate with the time in seconds. The water level of the lake drops by 16.36 centimeters when the gates are open for this duration, determined by dividing the volume of water by the lake's area and converting to centimeters.
Step-by-step explanation:
To address the question presented:
Demonstrate that 90 million liters of water flows out in 20 minutes.
Calculate the drop in the water level of the lake when the gates are open for 20 minutes in centimeters.
We start with the flow rate:
75,000 liters per second is the rate at which water is flowing out. To find the volume flowed out in 20 minutes, we need to convert 20 minutes into seconds and multiply by the flow rate:
20 minutes × 60 seconds/minute = 1,200 seconds
Now, we multiply the time by the flow rate:
1,200 seconds × 75,000 litres/second = 90,000,000 litres
This confirms that 90 million litres of water flows out in 20 minutes.
For the depth calculation, we know that one hectare is 10,000 m² and the area of the lake is 55 hectares. We convert the volume of water lost from litres to cubic metres:
90,000,000 litres ÷ 1,000 litres/cubic metre = 90,000 cubic metres
With the lake's area, we calculate the depth:
55 hectares × 10,000 m²/hectare = 550,000 m²
Divide the volume of water lost by the area of the lake to get the depth in metres:
90,000 m³ ÷ 550,000 m² = 0.1636 metres
Finally, convert this depth into centimetres:
0.1636 metres × 100 cm/metre = 16.36 centimetres
The water level of the lake drops by 16.36 centimetres when the gates are open for 20 minutes.