Units of Volume

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:

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: $Length\times ~width\times~height$

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:

$1~L=1~dm³=1,000~cm³$

$1~liter=1000~milliliters$

$1~milliliter = 1~cm³$

$1000~liters=1~m³$

Detailed explanation

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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 $\operatorname{cm}^3$ 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).

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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.

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Test your knowledge

Question 1

How many milliliters are in a liter?

Question 2

What is 18 liters written in milliliters?

Question 3

35.3 cm³ are? m³

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

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Identify the relationship between meters and centimeters.
Step 2: Convert from m³ to cm³ using the cubed conversion factor.
Step 3: Perform the calculation of the volume conversion.

Let's work through each step:
Step 1: We understand that 1 meter is equivalent to 100 centimeters.
Step 2: To convert cubic meters to cubic centimeters, we calculate $(100 \, cm/m)^3$ .
Step 3: Perform the calculation $100 \times 100 \times 100 = 1,000,000$ .

Therefore, the number of cubic centimeters in a cubic meter is $1,000,000 \, cm^3$ .

Answer

$1000000cm^3$

Exercise #2

How many milliliters are in a liter?

Video Solution

Step-by-Step Solution

To solve this conversion problem, follow these steps:

Step 1: Recognize the standard conversion in the metric system where 1 liter is equivalent to 1,000 milliliters.
Step 2: Apply this knowledge directly to the problem.

Let's work through the steps:

Step 1: Using the metric conversion, we know that 1 liter equals 1,000 milliliters. The metric system is based on powers of ten, which makes conversions straightforward. Here, 1 liter is defined as 1,000 milliliters because 'milli' signifies one-thousandth (1/1,000), making 1 liter = 1,000 * 1 ml.

Step 2: Therefore, applying the conversion to 1 liter yields:

$1 \text{ liter} = 1,000 \text{ milliliters}$

Therefore, the solution to the problem is $1,000ml$ .

Answer

$1,000ml$

Exercise #3

What is 18 liters written in milliliters?

Video Solution

Step-by-Step Solution

To convert 18 liters to milliliters, we will follow these steps:

Identify the conversion factor from liters to milliliters.
Multiply the given number of liters by this conversion factor.

Step 1: The conversion factor is $1 \text{ liter} = 1000 \text{ milliliters}$ .

Step 2: Multiply 18 liters by 1000 to convert it to milliliters:

$18 \times 1000 = 18000$ milliliters.

Thus, 18 liters is equal to $18,000$ milliliters.

Therefore, the correct answer is $\text{choice 3}: 18,000 \text{ ml}$ . The answer, when compared to the choices, confirms that choice 3 is indeed the correct one.

Answer

$18,000ml$

Exercise #4

35.3 cm³ are? m³

Video Solution

Step-by-Step Solution

To solve this problem, let's follow the necessary conversion steps:

Step 1: Identify the given volume in cubic centimeters. We have $35.3 \, \text{cm}^3$ .
Step 2: Use the conversion factor between cubic centimeters and cubic meters. We know that $1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3$ .
Step 3: Convert the given volume from cubic centimeters to cubic meters. To do this, divide the volume in cubic centimeters by 1,000,000:

$\frac{35.3 \, \text{cm}^3}{1,000,000} = \frac{35.3}{1,000,000} \, \text{m}^3$

Therefore, the equivalent volume in cubic meters is $\frac{35.3}{1,000,000} \, \text{m}^3$ .

Thus, the correct answer is:

$\frac{35.3}{1,000,000} \, \text{m}^3$

From the given choices, the correct choice is:

$\frac{35.3}{1,000,000m^3}$

Answer

$\frac{35.3}{1,000,000m^3}$

Exercise #5

What is 100 m³ written as cm³?

Video Solution

Step-by-Step Solution

To convert 100 m³ to cm³, follow these steps:

Step 1: Understand the relationship between meters and centimeters. We know that 1 meter equals 100 centimeters.
Step 2: Determine the volume in cubic centimeters for 1 cubic meter. Since 1 m = 100 cm, we have $1 \text{ m}^3 = (100 \, \text{cm})^3$ .
Step 3: Calculate $(100 \, \text{cm})^3$ . This results in $100 \times 100 \times 100 = 1,000,000$ cm³.
Step 4: Since we need to convert 100 m³, multiply the result for 1 m³ by 100. Thus, $100 \text{ m}^3 = 100 \times 1,000,000 \, \text{cm}^3 = 100,000,000 \, \text{cm}^3$ .

Therefore, 100 m³ is equivalent to $100,000,000 \, \text{cm}^3$ .

From the given choices, the correct choice is choice 3, which is $100,000,000 \, \text{cm}^3$ .

Answer

$100,000,000cm^3$

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?

Question 1

What is 100 m³ written as cm³?

Question 2

143535 milliliters are? liters

Question 3

Convert $$ 84cm^3 $$ into milliliters.

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Volume Measurements

Example 1

Example 2

Examples and exercises with solutions of volume units

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

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Volume Units