# Units of Volume

🏆Practice volume units

Every three-dimensional body has volume. For example, a ball or pyramid are bodies with volume. The volume of a body is our way of measuring the space that said body occupies in space.

For example, let's observe a cube whose length of each of its sides is $1\operatorname{cm}$, like this one:

To calculate the volume of the cube we will use the known formula: $Length\times ~width\times~height$

In this case, the three dimensions are equal and, therefore, we will note:

$V=1\operatorname{cm}\times1\operatorname{cm}\times1\operatorname{cm}=1\operatorname{cm}^3$

V is the letter used to abbreviate the word volume in exercises and is used to designate volumes.

That is, we found that the volume of the cube is $1~cm³=$ cubic centimeter (cm raised to the third power)

Known volume measurement units:

$1~m³=1000~dm³=1,000,000~cm³$

$1~dm³=1000~cm³$

Additionally, there are measurements that we primarily use for measuring liquids:

$1~L=1~dm³=1,000~cm³$

$1~liter=1000~milliliters$

$1~milliliter = 1~cm³$

$1000~liters=1~m³$

## Test yourself on volume units!

How many cm³ are there in a m³?

The function of volume units is to quantify or measure the volume of objects. Since it is a three-dimensional unit, these units are always expressed in cubic powers.

For example, cubic centimeter $\operatorname{cm}^3$ and cubic meter $\left(m^3\right)$. When referring to liquids, volume is usually measured in liters or gallons.

Let's analyze a simple exercise:

We have a box with the following measurements:

$Length~4~cm$

$Width~5~cm$

$Height~6~cm$

$4~\operatorname{cm}\times~5\operatorname{cm}\times~6\operatorname~{cm}=120$

$Length~4 ~cm\times ~width ~5 ~cm\times ~height ~6 ~cm$

if we need to calculate its volume.

In this case, the calculation is quite simple. We will calculate the volume of the box by multiplying the three measurements together. The result is $120~cm^3$. It is crucial to highlight that, because we multiply cm by cm by cm three times, the result is given in $\operatorname{cm}^3$, that is, cubic cm (cm raised to the third power).

If you are interested in this article, you may also be interested in the following articles:

On the Tutorela website you can find a variety of mathematics articles

## Volume Measurements

### Example 1

How many liters of water can the illustrated box hold?:

Let's remember that the formula to calculate the volume of a box is:

$Length\times width\times ~height$.

Let's calculate the volume of the box:

$V=1~m\times1m\times3~m=3~m^3$

$1~m³=1000~dm³=1,000,000~cm³$

We found that the volume of the box is $3~m³$ (cubic meters).

Now we must convert the result to liters to answer the question.

Let's remember that $1~m³=1000$ liters.

Therefore:

$3~m³=3000$ liters.

That is, the amount of water that we can pour into the box is $3000$ liters.

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today

### Example 2

How many liters are $10,000~cm³$?

Let's remember that:

$1,000~cm³=1 liter$

Therefore:

$10,000\operatorname{cm}³=10\times1000\operatorname{cm}³=10\times1~Liter=10~Liters$

That is, we found that $10,000~cm³$ are equivalent to $10$ liters.

## Examples and exercises with solutions of volume units

### Exercise #1

How many cm³ are there in a m³?

### Video Solution

$1000000cm^3$

### Exercise #2

Convert $6.8dm^3$ into milliliters.

### Video Solution

$6800ml$

### Exercise #3

How many milliliters are in a liter?

### Video Solution

$1,000ml$

### Exercise #4

What is 100 m³ written as cm³?

### Video Solution

$100,000,000cm^3$

### Exercise #5

143535 milliliters are? liters

### Video Solution

$143.535l$

## Review Questions

What are the units of volume?

As we have seen, everything that needs to be measured has its specific unit of measure. In the case of volume units, being a three-dimensional measure, that is, an object that has length, width, and height, its volume can be calculated. Therefore, we can measure it either in liters or milliliters, but if the objects have units of length, then the most common units in volume can be: $\operatorname{cm}^3$,$\operatorname{m}^3$,$\operatorname{dam}^3$,$\operatorname{hm}^3$,$\operatorname{dm}^3$,$\operatorname{mm}^3$, although it can also be measured in gallons and other volume units.

How are volume units written?

Being a unit of measure and as we said it is a three-dimensional unit, the measures are expressed to the third power, that is, as we have three dimensions length, width, and height, then suppose that its units are in $\operatorname{cm}$, then to calculate the volume it will be:

$\operatorname{cm}\times cm\times cm=cm^3$

If its lengths are $\operatorname{m}$, then the volume will be written in $\operatorname{m}^3$

What is the dimension of volume?

Being a dimension that is derived from length and by multiplying length, width, and height we will obtain a dimension to the cube. Or by making a conversion of volume units, that is, cubic, we can obtain an equivalence to liters, milliliters, or gallons.

Do you know what the answer is?