Questions: The water reservoir for a city is shaped like a rectangular prism 250 meters long, 60 meters wide, and 12 meters deep. At the end of the day, the reservoir is 70% full. How much water must be added overnight to fill the reservoir?

Solution Steps

To determine how much water must be added to fill the reservoir, we need to:

1. Calculate the total volume of the reservoir.
2. Calculate the current volume of water in the reservoir (70% of the total volume).
3. Subtract the current volume from the total volume to find the amount of water needed to fill the reservoir.

The total volume \( V \) of the reservoir can be calculated using the formula for the volume of a rectangular prism: \[ V = \text{length} \times \text{width} \times \text{depth} \] Substituting the given dimensions: \[ V = 250 \, \text{m} \times 60 \, \text{m} \times 12 \, \text{m} = 180000 \, \text{m}^3 \]

The current volume of water in the reservoir, which is \( 70\% \) full, is given by: \[ \text{Current Volume} = 0.70 \times V = 0.70 \times 180000 \, \text{m}^3 = 126000 \, \text{m}^3 \]

To find the amount of water that must be added to fill the reservoir, we subtract the current volume from the total volume: \[ \text{Water Needed} = V - \text{Current Volume} = 180000 \, \text{m}^3 - 126000 \, \text{m}^3 = 54000 \, \text{m}^3 \]

Final Answer