Volume of a Cube
Volume of a Cube is a Grade 8 math skill in Saxon Math Course 3, Chapter 5, where students calculate the volume of a cube using the formula V = s cubed, where s is the side length. Since all sides of a cube are equal, this is a special case of the rectangular prism formula, and students apply it to real-world contexts like packaging, storage, and construction.
Key Concepts
Property The formula for the volume ($V$) of a cube is the side length ($s$) cubed. $$V = s^3$$.
Examples A 3 foot cube of ice has a volume of $V = s^3 = (3 \text{ ft})^3 = 27 \text{ ft}^3$. A small box is a cube with edges that are 10 cm long. $V = s^3 = (10 \text{ cm})^3 = 1000 \text{ cm}^3$. A single die has an edge length of 2 cm. $V = s^3 = (2 \text{ cm})^3 = 8 \text{ cm}^3$.
Explanation A cube is the simplest 3D hero because all its sides are equal! Instead of multiplying length, width, and height separately, you just take the length of one side ($s$) and multiply it by itself three times. This awesome shortcut makes finding the volume of any cube, from a tiny sugar cube to a giant block of ice, incredibly fast.
Common Questions
What is the formula for the volume of a cube?
The volume of a cube is V = s cubed, where s is the length of any side. Since all sides of a cube are equal, you just raise the side length to the third power.
How is the cube volume formula a special case of the rectangular prism formula?
For a rectangular prism V = l times w times h. Since all sides of a cube are equal (l = w = h = s), the formula simplifies to V = s times s times s = s cubed.
What units are used for the volume of a cube?
Volume is always in cubic units. If the side length is in centimeters, the volume is in cubic centimeters.
How do you find the side length of a cube if you know its volume?
Take the cube root of the volume. For example, if V = 125 cubic centimeters, then s = cube root of 125 = 5 centimeters.
Where is volume of a cube taught in Grade 8?
Volume of a cube is covered in Saxon Math Course 3, Chapter 5: Number and Operations and Algebra.