Volume Of A Rectangular Prism

🔑 Key Concepts

  • The rectangular prism measures \(4\) units by \(3\) units by \(5\) units.
  • The base contains \(4\times3=12\) square units.
  • A one-unit-high layer contains \(12\) cubic units.
  • The prism contains \(5\) identical layers.
  • The total volume is \(12\times5=60\) cubic units.
  • The formula \(V=lwh\) gives \(V=4\times3\times5=60\).
  • The equivalent formula \(V=Bh\) gives \(V=(12)(5)=60\).

✏️ Interactive Worked Example

🧠 Math Vocabulary

  • Rectangular prism: A three-dimensional solid with six rectangular faces.
  • Length: One horizontal dimension of a rectangular prism.
  • Width: The second horizontal dimension of a rectangular prism.
  • Height: The perpendicular distance between the prism’s congruent bases.
  • Dimension: A measurable direction, such as length, width, or height.
  • Base: A selected face of a three-dimensional solid.
  • Base area: The area of a selected base, represented by \(B\).
  • Layer: One complete horizontal level of unit cubes.
  • Unit cube: A cube whose length, width, and height are each one unit.
  • Volume: The amount of three-dimensional space contained inside a solid.
  • Cubic unit: A unit used to measure three-dimensional volume.
  • Formula: A mathematical rule that shows the relationship among quantities.
  • Product: The result of multiplication.

💡 Main Idea

A \(4\times3\) base contains \(12\) unit cubes in each layer. A height of \(5\) units creates five identical layers, so the prism contains \(12\times5=60\) unit cubes. This is represented by both \(V=lwh\) and \(V=Bh\).

📚 What You Should Already Know

Students should know how to find the area of a rectangle, multiply whole numbers, identify the length, width, and height of a rectangular prism, and distinguish between square units and cubic units.

🚀 What Comes Next

Students can extend this reasoning to rectangular prisms with fractional or decimal dimensions, solve for missing dimensions, compare prisms with equal volumes, and apply the general prism formula \(V=Bh\).

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