To solve this problem, we need to calculate the total volume of the reservoir and then determine how much water is required to fill it to capacity based on the information provided.

Step 1: Calculate the total volume of the reservoir

The reservoir is shaped like a rectangular prism, so the volume $V$ is given by:

$V = \text{length} \times \text{width} \times \text{depth}$

Substituting the values:

$V = 260 \, \text{m} \times 80 \, \text{m} \times 14 \, \text{m} = 291,200 \, \text{m}^3$

Step 2: Determine the current volume of water

The reservoir is currently 65% full, so the volume of water currently in the reservoir is:

$V_{\text{current}} = 0.65 \times 291,200 \, \text{m}^3 = 189,280 \, \text{m}^3$

Step 3: Calculate the volume of water needed to fill the reservoir

The amount of water required to fill the reservoir is the difference between the total volume and the current volume:

$V_{\text{needed}} = 291,200 \, \text{m}^3 - 189,280 \, \text{m}^3 = 101,920 \, \text{m}^3$

Conclusion:

To fill the reservoir, 101,920 cubic meters of water must be added overnight.

Would you like more details or have any questions?

Related questions:

1. What is the formula for the volume of a rectangular prism?
2. How would the problem change if the reservoir was only 50% full?
3. How do we calculate the volume if the reservoir had a different shape, such as a cylinder?
4. What would happen if the depth of the reservoir increased to 20 meters?
5. How does the percentage full affect the amount of water required?

Tip:

Always ensure the units are consistent when calculating volume to avoid mistakes!