Volume of a Cube
The volume of a cube in Grade 7 is found using the formula V = s³, where s is the edge length. Because all three dimensions of a cube are equal, the formula V = s × s × s = s³ applies. In Saxon Math, Course 2, a cube with 5-inch edges has volume = 5³ = 125 in³. The exponent 3 reflects the three-dimensional nature of volume. This formula also introduces students to cubing numbers — an important concept in algebra — and cubic units of measurement used in science and engineering.
Key Concepts
Property A cube is a special rectangular prism where the length, width, and height are all the same. If the edge length is $s$, the volume formula is: $$V = s \times s \times s = s^3$$.
Examples A cube with an edge length of 5 inches has a volume of $V = 5 \text{ in} \times 5 \text{ in} \times 5 \text{ in} = 125 \text{ in}^3$. A cube with 10 cm sides has a volume of $V = 10 \text{ cm} \times 10 \text{ cm} \times 10 \text{ cm} = 1000 \text{ cm}^3$.
Explanation A cube is the chillest of all rectangular prisms because all its sides are equal! So, instead of juggling length, width, and height, you just need one number: the length of any edge. Multiply that number by itself three times (or cube it), and you have got the volume. Easy peasy lemon squeezy!
Common Questions
What is the formula for the volume of a cube?
V = s³, where s is the length of one edge. Since all edges of a cube are equal, this equals s × s × s.
Why do you cube the edge length to find volume?
Volume measures three-dimensional space. For a cube, all three dimensions (length, width, height) are equal to s, so multiplying them gives s × s × s = s³.
What is the volume of a cube with edge length 10 cm?
V = 10³ = 10 × 10 × 10 = 1000 cm³.
How is a cube different from a rectangular prism?
A cube is a special rectangular prism where all edges are equal in length. A regular rectangular prism can have different lengths, widths, and heights.
Where is volume of a cube taught in Saxon Math Course 2?
The volume of a cube is covered in Saxon Math, Course 2, as part of Grade 7 three-dimensional geometry and measurement content.
What are the units for volume of a cube?
The units are always cubic — for example, cm³, in³, ft³, or m³. If the edge is measured in centimeters, volume is in cubic centimeters.
What common mistakes do students make with cube volume?
Students sometimes multiply s × 3 instead of s × s × s, confusing 3s with s³. Always cube the edge length, do not multiply it by 3.