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 \(= \ S\)

Cube

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

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