What Are Volume and Surface Area?

Before we dive into formulas, let's make sure we understand what we're actually measuring.

Volume

The amount of three-dimensional space enclosed inside a solid shape. Volume is measured in cubic units such as $cm^{3}$ , $m^{3}$ , or $mm^{3}$ .

Surface Area

The total area of all the outer faces (surfaces) of a three-dimensional shape. Surface area is measured in square units such as $cm^{2}$ , $m^{2}$ , or $mm^{2}$ .

Analogy

Think of volume as how much water you could pour inside a box until it's completely full. Think of surface area as how much wrapping paper you'd need to cover every side of that box — no gaps, no overlaps.

These two measurements tell us very different things about a 3D shape:

Volume → capacity, how much fits inside
Surface area → the amount of material covering the outside

The Cube

Cube

A three-dimensional shape with 6 identical square faces, 12 equal edges, and 8 vertices. Every edge has the same length.

Let the length of each edge be $s$ .

Volume of a Cube

Since all three dimensions are equal:
$V = s \times s \times s = s^{3}$

Surface Area of a Cube

A cube has 6 identical square faces, each with area $s^{2}$ :
$S A = 6 s^{2}$

Example

Example: A Rubik's cube has an edge length of $5.7 cm$ . Find its volume and surface area.

Volume:
$V = s^{3} = 5. 7^{3} = 5.7 \times 5.7 \times 5.7 = 185.193 cm^{3}$

Surface Area:
$S A = 6 s^{2} = 6 \times 5. 7^{2} = 6 \times 32.49 = 194.94 cm^{2}$

Exam Tip

Remember: $s^{3}$ means " $s$ cubed" — this is actually where the word cube in mathematics comes from!

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