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

Units of Volume | Tutorela

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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Test yourself on volume units!

Convert $$ 16,848dm^3 $$ into liters.

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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

Convert $$ 6.8dm^3 $$ into milliliters.

Question 2

Convert $$ 3850ml $$ into cubic decimeters.

Question 3

Convert $61\frac{1}{2}cm^3$ into cubic decimeter.

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

Convert $16,848dm^3$ into liters.

Video Solution

Step-by-Step Solution

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

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the conversion

Now, let's work through each step:
Step 1: The problem provides us with the volume $16,848 \, \text{dm}^3$ .
Step 2: We know that $1 \, \text{dm}^3 = 1 \, \text{l}$ . This means that each cubic decimeter is equivalent to one liter.
Step 3: Using this direct equivalence, we can convert $16,848 \, \text{dm}^3$ directly into $16,848 \, \text{l}$ .

Therefore, the volume of $16,848 \, \text{dm}^3$ is equivalent to $16,848 \, \text{l}$ .

Answer

$16,848l$

Exercise #2

Convert $6.8dm^3$ into milliliters.

Video Solution

Step-by-Step Solution

To convert $6.8dm^3$ into milliliters, we'll follow these steps:

Step 1: Identify the given volume in cubic decimeters, which is $6.8dm^3$ .
Step 2: Use the conversion factor that $1dm^3 = 1000ml$ .
Step 3: Multiply the given volume by the conversion factor to convert cubic decimeters to milliliters.

Now, let's perform the conversion:
Given: $6.8dm^3$

Using the conversion factor, we calculate:
$6.8dm^3 \times 1000ml/dm^3 = 6800ml$

Therefore, the volume of $6.8dm^3$ is equivalent to $6800ml$ .

Answer

$6800ml$

Exercise #3

Convert $3850ml$ into cubic decimeters.

Video Solution

Step-by-Step Solution

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

Step 1: Identify the given amount in milliliters which is $3850 \, \text{ml}$ .
Step 2: Use the conversion factor $1 \, \text{dm}^3 = 1000 \, \text{ml}$ .
Step 3: Divide the milliliters by 1000 to convert to cubic decimeters.

Now, let's work through each step:
Step 1: We have $3850 \, \text{ml}$ .
Step 2: We need to convert this volume to cubic decimeters using the conversion factor where $1000 \, \text{ml} = 1 \, \text{dm}^3$ .
Step 3: Perform the conversion by dividing the milliliters by the conversion factor:

$\frac{3850 \, \text{ml}}{1000 \, \text{ml/dm}^3} = 3.85 \, \text{dm}^3$

Therefore, the solution to the problem is $3.85 \, \text{dm}^3$ .

Answer

$3.85dm^3$

Exercise #4

Convert $61\frac{1}{2}cm^3$ into cubic decimeter.

Video Solution

Step-by-Step Solution

Let's solve the problem through a series of steps for ease of understanding:

Step 1: Identify the volume in cubic centimeters.
The given volume is $61\frac{1}{2} \, \text{cm}^3$ .
Step 2: Convert the mixed number to an improper fraction.
The mixed number $61\frac{1}{2}$ can be rewritten as $61 + \frac{1}{2}$ which equals $\frac{122}{2} + \frac{1}{2} = \frac{123}{2}$ . This is equivalent to 61.5 cubic centimeters.
Step 3: Convert cubic centimeters to cubic decimeters.
Using the fact that $1 \, \text{dm}^3 = 1000 \, \text{cm}^3$ , we divide the given volume by 1000 to convert from cubic centimeters to cubic decimeters.
$\frac{123}{2} \div 1000 = \frac{123}{2000} = \frac{61.5}{1000}$

Therefore, the volume in cubic decimeters is $\frac{61.5}{1000} \, \text{dm}^3$ .

Upon examining the available choices, choice 1: $\frac{61.5}{1000 \, \text{dm}^3}$ is the correct answer.

The solution to the problem is $\frac{61.5}{1000 \, \text{dm}^3}$ .

Answer

$\frac{61.5}{1000dm^3}$

Exercise #5

Convert $1.6l$ into milliliters.

Video Solution

Step-by-Step Solution

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

Step 1: Identify the conversion factor between liters and milliliters.
Step 2: Perform the conversion by multiplying the volume in liters by 1000 since $1 \text{ liter} = 1000 \text{ milliliters}$ .

Now, let's work through each step:
Step 1: The conversion factor is $1 \text{ liter} = 1000 \text{ milliliters}$ .
Step 2: We have $1.6 \text{ liters}$ . To convert this into milliliters, multiply $1.6$ by $1000$ :

$1.6 \times 1000 = 1600$

Therefore, the solution to the problem is $1600 \text{ ml}$ .

The correct choice from the given options is: $1600 \text{ ml}$ .

Answer

$1600ml$

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

Convert $$ 1.6l $$ into milliliters.

Question 2

Convert $$ 31m^3 $$ into litres.

Question 3

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

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Units of Volume

Test yourself on volume units!

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

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Volume Units