Is a cube a rectangular prism?

Yes. A cube is a rectangular prism where length, width and height are equal. That is why $V = l \times w \times h$ becomes $V = s \times s \times s$.

How do I find the edge if I only know the volume?

Find the number that multiplied by itself 3 times gives the volume. That is the cube root: $\sqrt[3]{125} = 5$ because $5^3 = 125$. Learning the perfect cubes up to $1000$ makes this fast.

What if the edge is a fraction?

The formula works the same way: $\left(\frac{1}{2}\right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$. A cube with a half-unit edge has one eighth of a cubic unit of volume.

Teacher Resources

Volume of Cubes

Q: Why is $s^3$ called "s cubed"?

Because $s \times s \times s$ is exactly the volume of a cube with edge $s$. The name of the power comes from the shape!

Learn to find the volume of a cube with V = s³, work with whole and decimal edges, find the edge from the volume and link cm³ to liters.

Elementary20 minLesson

Printable worksheet

Definition

A cube is a 3D shape with 6 identical square faces. All 12 of its edges have the same length, which we call

s

The volume of a cube is the amount of space inside it. You already know that a rectangular prism has

V = l \times w \times h

. A cube is the special case where length, width and height are all the same number

s

V = s \times s \times s = s^3

We read

s^3

as "

s

cubed". Volume is always written in cubic units: if the edge is in cm, the volume is in cm³; if the edge is in m, the volume is in m³.

The numbers you get by cubing whole numbers are called perfect cubes (or cube numbers):

1,\ 8,\ 27,\ 64,\ 125,\ 216,\ 343,\ 512,\ 729,\ 1000

Going backwards, from the volume to the edge, is called taking the cube root:

s = \sqrt[3]{V}

. For example,

\sqrt[3]{64} = 4

because

4 \times 4 \times 4 = 64

Try it now

Which formula gives the volume of a cube with edge

s

Worked Examples

A wooden block is a cube with an edge of $5$ cm. What is its volume?

Write the cube formula

$V = s^3 = s \times s \times s$ → Formula ready

Substitute the edge

$V = 5 \times 5 \times 5$ → Value plugged in

Multiply the first two edges

$5 \times 5 = 25$ → Area of one face: $25$ cm²

Multiply by the third edge

$25 \times 5 = 125$ → $V = 125$ cm³

Answer: The volume of the block is $125$ cm³.

Common Mistakes

Multiplying the edge by 3: for $s = 5$ , writing $V = 5 \times 3 = 15$

Why it's wrong: $s^3$ means $s$ multiplied by itself 3 times, not $s$ times 3.

Correct: $5^3 = 5 \times 5 \times 5 = 125$ cm³.

Stopping after two edges: $5 \times 5 = 25$

Why it's wrong: $s \times s$ is the area of ONE face (square units). Volume needs all three dimensions.

Correct: Multiply by the edge one more time: $25 \times 5 = 125$ cm³, and write cubic units.

Thinking that doubling the edge doubles the volume

Why it's wrong: The edge appears three times in $s \times s \times s$ , so each of the three factors doubles.

Correct: Doubling the edge multiplies the volume by $2^3 = 8$ . Tripling it multiplies the volume by $3^3 = 27$ .

Misplacing the decimal point: $0.2^3 = 0.8$ or $0.6$

Why it's wrong: Each multiplication by a decimal adds decimal places: one decimal place three times gives three decimal places.

Correct: $0.2 \times 0.2 = 0.04$ , then $0.04 \times 0.2 = 0.008$ . A small edge gives an even smaller volume.

Interactive Visual

3D Shape Viewer

Rotate X (20°)

Rotate Y (30°)

Length (5)

Faces

Edges

Vertices

Euler's formula: F + V − E = 6 + 8 − 12 = 2

Volume

V = s³

V = 5³ = 125

125 cm³

Surface Area

SA = 6s²

SA = 6 · 5² = 150

150 cm²

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

18 problems

Problem 1 of 18

Easy

Which formula gives the volume of a cube with edge $s$ ?

Why It Matters

Cubes are everywhere, and their volume is the easiest one to calculate:

Kitchen: an ice cube with a 3 cm edge holds $27$ cm³ of water
Liters: a cube with a 10 cm edge holds exactly $1000$ cm³, which is 1 liter. This is how the liter is defined!
Packing: shipping boxes, storage cubes and dice are all cubes
Building: concrete blocks, cubic tanks and cube-shaped rooms
Scaling: when a cube gets 2 times bigger on every edge, it holds 8 times as much. Knowing this helps you guess sizes and avoid costly mistakes.

The cube formula is also the first step toward cylinders, cones, spheres and pyramids, which you will meet in the next lessons.

Real World Applications

Ice Cube Trays

Ice cube trays make small cubes of ice. Knowing the volume of one cube tells you how much water a whole tray needs.

Example:

An ice cube with a $2$ cm edge holds $2^3 = 8$ cm³ of water.

1Try It Yourself

A tray makes $12$ ice cubes. Each cube has an edge of $3$ cm.

How many cm³ of water do you need to fill the whole tray?

Step 1: Write the mathematical expression

Find the volume of one cube, then multiply by 12:

Storage Cubes

Fabric storage cubes for shelves come in cube shapes. Their volume in liters tells you how much they can hold.

Example:

A storage cube with a $10$ cm edge holds $1000$ cm³, which is exactly $1$ liter.

2Try It Yourself

A storage cube has an edge of $40$ cm.

How many liters does it hold? ( $1$ L $= 1000$ cm³)

Step 1: Write the mathematical expression

Cube the edge, then divide by 1000:

Toy Building Blocks

Toy companies pack small cube blocks into larger cube boxes. The box must hold a whole number of blocks along each edge.

Example:

A box with a $6$ cm edge holds $3 \times 3 \times 3 = 27$ blocks with a $2$ cm edge.

3Try It Yourself

A cube-shaped box has an inside edge of $10$ cm. It is filled with toy cubes that have a $2$ cm edge.

How many toy cubes fit in the box?

Step 1: Write the mathematical expression

Count the blocks along one edge, then cube that number:

Key Takeaways

1A cube has 6 equal square faces and 12 equal edges of length $s$
2Volume of a cube: $V = s \times s \times s = s^3$ , the special case of $l \times w \times h$
3Always write cubic units: cm³, m³, in³
4Perfect cubes to know: $1, 8, 27, 64, 125, 216, 343, 512, 729, 1000$
5To find the edge from the volume, take the cube root: $s = \sqrt[3]{V}$
6Doubling the edge multiplies the volume by $8$ ; a cube with a $10$ cm edge holds $1$ liter

Frequently Asked Questions

Because

s \times s \times s

is exactly the volume of a cube with edge

s

. The name of the power comes from the shape!

Glossary

Cube: A 3D shape with 6 identical square faces, 12 equal edges and 8 vertices
Edge: A line segment where two faces meet; in a cube all edges have the same length $s$
Cubic unit: The volume of a cube with a 1-unit edge, such as 1 cm³ or 1 m³
Perfect cube: A number that is a whole number cubed, such as $27 = 3^3$ or $64 = 4^3$
Cube root: The number that, cubed, gives a value: $\sqrt[3]{216} = 6$ because $6^3 = 216$

Formula Card

Volume of a cube

V = s^3 = s \times s \times s

Multiply the edge by itself three times

Edge from volume

s = \sqrt[3]{V}

Find the number that, cubed, gives the volume

Scaling the edge

(k \cdot s)^3 = k^3 \cdot s^3

Edge times 2 gives volume times 8; edge times 3 gives volume times 27

The liter cube

10^3 = 1000 \text{ cm}^3 = 1 \text{ L}

A cube with a 10 cm edge holds exactly 1 liter

Volume of Cubes

Definition

Worked Examples

Common Mistakes

Interactive Visual

3D Shape Viewer

Interactive Sandbox

Expression Calculator

History

Practice Problems

Why It Matters

Real World Applications

Ice Cube Trays

Storage Cubes

Toy Building Blocks

Key Takeaways

Frequently Asked Questions

Glossary

Formula Card

Volume of a cube

Edge from volume

Scaling the edge

The liter cube

More in This Topic

Introduction to Volume

Metric Volume Units (mL, L)

Volume of Rectangular Prisms

Imperial Volume Units (cups, pints, gallons)