## How to Find the Volume of a Cube

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### What Is A Cube?

A cube is a **three-dimensional** solid that has six **square** faces that are the same and meet at right angles, eight corners, and twelve sides that are all the same length. One of the 5 Platonic Solids is a cube, also known as a **hexahedron**.

There are three sides to a cube:

**Length**is usually considered the**bigger**of the "flat" measurements.**Width**is usually the**shorter**of the two "flat" measurements.**Height**or depth is the dimension that gives a shape three-dimensionality.

### How to Find the Volume of a Cube

The length of each edge of the cube is the same.

\(V \ = \ w.l.h\), width \(=\) length \(=\) height \(= \ S\)

**Simplify the formula so:**

\(V \ = \ s^3\)

### How to Calculate Volume Based on Area

Here's another problem to solve. What if the **area** of one side of a cube is given? Can you figure out the volume from that?

**Yes**, the area of a face is equal to the \(length \times Width\) of the face. Once you know how long or wide something is, you can use the volume formula:

- Find the
**square**root of the given area measurement. This will tell you the**length**of any side. - Use the volume
**formula**to figure out how big the volume is \(V \ = \ s^3\).

### Example 1:

Find the cube's volume if each side is \(7\) cm long.

**Solution:**

Given that each side of the cube is \(7\) cm long. We know that a cube's volume is equal to (its sides' length)\(^3\).

So, the volume, \(V\), is equal to \((7 \ cm)^3\) \(⇒ \ V \ = \ 343 \ cm^3\)

### Example 2:

If one side of a cube has an area of \(187.69\), what is the cube's volume?

**Solution:**

Given that one side of the cube has an area of \(187.69\), We know that the area of one side of a cube is equal to the length of its sides **squared.**

So, the length of any side, S, equals: \(S \ = \ \sqrt{187.69} \ = \ 13.7\)

So, Volume, \(= \ (13.7)^2\)

### Exercises for Volume of Cubes

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## Volume of Cubes Practice Quiz

### More Solid Figures courses

- How to Find the Volume of a Rectangular Prism
- How to Find the Volume of a Cylinder
- How to Find the Surface Area of a Cylinder
- How to Find the Surface Area of a Rectangular Prism
- How to Find Volume and Surface Area of Cubes
- How to Find the Volume of a Cube
- How to Find Volume and Surface Area of Pyramids and Cone