 ## How to Find the Volume of a Cube

### 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

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 1) $$\color{red}{2744}$$ in$$^3$$ 2) $$\color{red}{343}$$ cm$$^3$$ 3) $$\color{red}{1}$$ mm$$^3$$ 4) $$\color{red}{512}$$ ft$$^3$$ 5) $$\color{red}{3375}$$ m$$^3$$ 6) $$\color{red}{4096}$$ mm$$^3$$ 7) $$\color{red}{729}$$ in$$^3$$ 8) $$\color{red}{8}$$ cm$$^3$$ 9) $$\color{red}{4913}$$ cm$$^3$$ 10) $$\color{red}{27}$$ ft$$^3$$ ## Volume of Cubes Practice Quiz

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