🔑 Key Concepts
- The volume of a rectangular prism is found using \(V=lwh\).
- Multiplying the length and width gives the area of the rectangular base.
- A \(9\)-inch by \(5\)-inch base contains \(45\) square inches.
- Each one-inch-high layer contains \(45\) cubic inches.
- Seven identical layers contain \(45\times7=315\) cubic inches.
- The formulas \(V=lwh\) and \(V=Bh\) describe the same relationship.
✏️ Interactive Worked Example
🧠 Math Vocabulary
- Rectangular prism: A three-dimensional solid with six rectangular faces.
- Length: One horizontal dimension of the rectangular prism.
- Width: The second horizontal dimension of the rectangular prism.
- Height: The perpendicular distance between the prism’s two congruent bases.
- Dimension: A measurable direction, such as length, width, or height.
- Base: A selected face of a three-dimensional solid used to organize a volume calculation.
- Base area: The area of the selected base, represented by \(B\).
- Layer: One complete level of unit cubes covering the base.
- Unit cube: A cube with edge lengths of one unit.
- Volume: The amount of three-dimensional space contained inside a solid.
- Square inch: A unit used to measure area, written as \(\text{in}^2\).
- Cubic inch: A unit used to measure volume, written as \(\text{in}^3\).
- Capacity: The amount that a three-dimensional container can hold.
💡 Main Idea
Multiplying the length and width of a rectangular prism gives the area of its base. In this example, the \(9\)-inch by \(5\)-inch base contains \(45\) square inches. Each one-inch-high layer therefore contains \(45\) cubic inches. Stacking seven layers gives a total volume of \(315\) cubic inches.
📚 What You Should Already Know
Students should know how to find the area of a rectangle, multiply whole numbers, identify the dimensions of a rectangular prism, and distinguish between square units and cubic units.
🚀 What Comes Next
Students can extend this reasoning by solving for missing dimensions, comparing rectangular prisms with equal volumes, working with fractional or mixed-number edge lengths, and applying the general prism formula \(V=Bh\).
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