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 1cm 1\operatorname{cm} , like this one:

a cube whose length of each of its sides is 1 cm

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

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

V=1cm×1cm×1cm=1cm3 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= 1~cm³= cubic centimeter (cm raised to the third power)

Known volume measurement units:

1 m3=1000 dm3=1,000,000 cm3 1~m³=1000~dm³=1,000,000~cm³

1 dm3=1000 cm3 1~dm³=1000~cm³

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

1 L=1 dm3=1,000 cm3 1~L=1~dm³=1,000~cm³

1 liter=1000 milliliters 1~liter=1000~milliliters

1 milliliter=1 cm3 1~milliliter = 1~cm³

1000 liters=1 m3 1000~liters=1~m³


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How many cm³ are there in a m³?

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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 cm3 \operatorname{cm}^3 and cubic meter (m3) \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 cmLength~4~cm

Width 5 cmWidth~5~cm

Height 6 cm Height~6~cm

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

Length 4 cm× width 5 cm× height 6 cm 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 cm3 120~cm^3 . It is crucial to highlight that, because we multiply cm by cm by cm three times, the result is given in cm3 \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:

  • Units of length
  • Units of weight
  • Units of time
  • Monetary units
  • Surface units

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?:

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×width× height Length\times width\times ~height .

Let's calculate the volume of the box:

V=1 m×1m×3 m=3 m3 V=1~m\times1m\times3~m=3~m^3

1 m3=1000 dm3=1,000,000 cm3 1~m³=1000~dm³=1,000,000~cm³

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

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

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

Therefore:

3 m3=3000 3~m³=3000 liters.

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


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Example 2

How many liters are 10,000 cm3 10,000~cm³ ?

Let's remember that:

1,000 cm3=1liter 1,000~cm³=1 liter

Therefore:

10,000cm3=10×1000cm3=10×1 Liter=10 Liters 10,000\operatorname{cm}³=10\times1000\operatorname{cm}³=10\times1~Liter=10~Liters

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


Examples and exercises with solutions of volume units

Exercise #1

How many cm³ are there in a m³?

Video Solution

Answer

1000000cm3 1000000cm^3

Exercise #2

Convert 6.8dm3 6.8dm^3 into milliliters.

Video Solution

Answer

6800ml 6800ml

Exercise #3

How many milliliters are in a liter?

Video Solution

Answer

1,000ml 1,000ml

Exercise #4

What is 100 m³ written as cm³?

Video Solution

Answer

100,000,000cm3 100,000,000cm^3

Exercise #5

143535 milliliters are? liters

Video Solution

Answer

143.535l 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: cm3 \operatorname{cm}^3 ,m3 \operatorname{m}^3 ,dam3 \operatorname{dam}^3 ,hm3 \operatorname{hm}^3 ,dm3 \operatorname{dm}^3 ,mm3 \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 cm \operatorname{cm} , then to calculate the volume it will be:

cm×cm×cm=cm3 \operatorname{cm}\times cm\times cm=cm^3

If its lengths are m \operatorname{m} , then the volume will be written in m3 \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.


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