🔑 Key Concepts
- The swimming pool measures \(20\) feet by \(24\) feet by \(15\) feet.
- Two-thirds of the \(15\)-foot height is \(10\) feet.
- The base area is \(20\times24=480\) square feet.
- At a water depth of \(10\) feet, the water volume is \(480\times10=4{,}800\) cubic feet.
- The water costs \(0.04\) USD per cubic foot.
- The total cost is \(4{,}800\times0.04=192.00\) USD.
- Only the water-filled portion is used in the cost calculation.
✏️ Interactive Worked Example
🧠 Math Vocabulary
- Rectangular prism: A three-dimensional solid with six rectangular faces.
- Volume: The amount of three-dimensional space contained inside a solid.
- Capacity: The amount a container can hold.
- Cubic foot: The volume of a cube with one-foot edge lengths, written as \(\text{ft}^3\).
- Base area: The area of a selected base, represented by \(B\).
- Water depth: The vertical height of the water inside a container.
- Fraction filled: The part of a container’s full capacity currently occupied.
- Unit rate: A rate comparing a quantity to one unit, such as \(0.04\) USD per cubic foot.
- Cost per cubic foot: The price charged for each cubic foot of water.
- Partial volume: The volume of only the occupied portion of a container.
- Two-thirds: Two of three equal parts, represented by \(\frac{2}{3}\).
- Product: The result of multiplication.
- Constant: A quantity that remains unchanged, such as the pool’s base area.
💡 Main Idea
A pool filled two-thirds of its \(15\)-foot height contains water to a depth of \(10\) feet. Multiplying the \(20\)-foot length, \(24\)-foot width, and \(10\)-foot water depth gives \(4{,}800\) cubic feet of water. At \(0.04\) USD per cubic foot, the total cost is \(192.00\) USD.
📚 What You Should Already Know
Students should know how to calculate the volume of a rectangular prism, multiply fractions by whole numbers, interpret cubic units, multiply decimals, and use a unit rate to calculate a total cost.
🚀 What Comes Next
Students can extend this reasoning to containers filled to other fractional depths, changing unit prices, missing dimensions, unit conversions, and multistep applications involving volume, capacity, cost, and rates.
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