The question asks for the amount of hydroelectric power produced, given that the power produced by a dam is proportional to the flow rate of water. Specifically, it provides:

• Known values: 35,700 kW of power is produced when the flow rate is 2260 cubic feet per second (ft³/s).
• Find: The power produced when the flow rate is 2180 ft³/s.

Since power is proportional to the flow rate, we can set up a ratio between the two scenarios. This can be solved using direct proportion.

The ratio is:

$\frac{35,700 \text{ kW}}{2260 \text{ ft}^3/\text{s}} = \frac{x \text{ kW}}{2180 \text{ ft}^3/\text{s}}$

Now, solve for $x$:

$x = \frac{35,700 \times 2180}{2260}$

I'll calculate that for you.The amount of power produced when the flow rate is 2180 ft³/s is approximately 34,436 kW.

Do you have any questions, or would you like a detailed breakdown of the solution? Here are five related questions to consider:

1. How does proportionality help in solving real-world problems?
2. What would happen if the flow rate increased by 10%?
3. How would you calculate the power for a different flow rate, such as 2000 ft³/s?
4. What does "direct proportionality" mean in mathematical terms?
5. How would errors in measuring the flow rate affect the power calculation?

Tip: In problems involving proportionality, always make sure to maintain the ratio correctly between known and unknown values!