Volume Of A Cube

🔑 Key Concepts

  • A cube has equal length, width, and height.
  • The cube in this lesson measures \(4\) centimeters on every edge.
  • One horizontal layer contains \(4\times4=16\) unit cubes.
  • The cube contains \(4\) identical layers.
  • The total number of unit cubes is \(16\times4=64\).
  • The volume formula for a cube is \(V=s^3\).
  • For this cube, \(V=4^3=4\times4\times4=64\text{ cm}^3\).

✏️ Interactive Worked Example

🧠 Math Vocabulary

  • Cube: A three-dimensional solid with six congruent square faces and equal edge lengths.
  • Edge length: The distance from one vertex to the next along an edge of a solid.
  • Volume: The amount of three-dimensional space contained inside a solid.
  • Unit cube: A cube whose length, width, and height are each one unit.
  • Cubic centimeter: The volume of a cube with one-centimeter edge lengths, written as \(\text{cm}^3\).
  • Layer: One complete horizontal level of unit cubes.
  • Base: A selected face of a three-dimensional solid.
  • Base area: The area of the selected base, represented by \(B\).
  • Exponent: A number showing how many times a base is used as a factor.
  • Cube of a number: The product of a number multiplied by itself three times.
  • Congruent: Having the same shape and measurements.
  • Dimension: A measurable direction, such as length, width, or height.

💡 Main Idea

A cube with an edge length of \(4\) centimeters contains \(4\times4=16\) unit cubes in each layer and four layers altogether. Therefore, the cube contains \(16\times4=64\) cubic-centimeter units. This is represented by the formula \(V=s^3=4^3=64\text{ cm}^3\).

📚 What You Should Already Know

Students should know how to find the area of a square, multiply whole numbers, interpret exponents, identify the equal edge lengths of a cube, and distinguish square units from cubic units.

🚀 What Comes Next

Students can extend this reasoning to cubes with fractional or decimal edge lengths, solve for missing edge lengths when the volume is known, compare cubes of different sizes, and apply volume formulas in real-world problems.

🧩 Embed This Video in Your LMS

Teachers can embed this video directly into Canvas, Google Classroom, Schoology, or another learning platform.