Volume Units - Examples, Exercises and Solutions

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 $16,848 \, \text{l}$.

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 $6800ml$.

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 $3.85 \, \text{dm}^3$.

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 $\frac{61.5}{1000 \, \text{dm}^3}$.

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: $1600 \text{ ml}$.

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

• Step 1: Identify the conversion factor.
• Step 2: Apply the conversion factor to the given volume in cubic meters.
• Step 3: Calculate the corresponding volume in liters.

Now, let's work through each step:

Step 1: We know that $1 \, m^3$ is equivalent to $1000 \, l$.

Step 2: We have a volume of $31 \, m^3$. To convert this to liters, we multiply the given volume by the conversion factor:

$31 \, m^3 \times 1000 \, \frac{l}{m^3} = 31000 \, l$.

Step 3: Hence, the volume of $31 \, m^3$ is $31000 \, l$.

Therefore, the solution to the problem is $31000 \, l$.

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

• Step 1: Recognize the equivalence $1 \, \text{cm}^3 = 1 \, \text{ml}$.
• Step 2: Apply the conversion to the given volume.

Now, let's work through the solution:

Step 1: We know that $1 \, \text{cm}^3$ is equal to $1 \, \text{ml}$. This is a standard conversion where every cubic centimeter corresponds exactly to one milliliter.

Step 2: Given the volume of $84 \, \text{cm}^3$, we apply the conversion factor:
$84 \, \text{cm}^3 = 84 \times 1 \, \text{ml} = 84 \, \text{ml}.$

Thus, the volume of $84 \, \text{cm}^3$ is equivalent to $84 \, \text{ml}$.

Therefore, the solution to the problem is $84 \, \text{ml}$.

To solve the problem of converting 143535 milliliters to liters, follow these steps:

• The given quantity is 143535 milliliters (ml).
• Use the conversion factor: $1 \text{ liter} = 1000 \text{ milliliters}$.
• Convert milliliters to liters by dividing the milliliters by 1000.

Let's perform the calculation:
$143535 \text{ ml} \div 1000 = 143.535 \text{ liters}$

This calculation shows that 143535 milliliters equals 143.535 liters.

Therefore, the solution to the problem is $143.535l$.

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 $100,000,000 \, \text{cm}^3$.

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:

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

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.

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 $1,000ml$.

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 $1,000,000 \, cm^3$.

To solve this problem, we will convert the 160 milliliters to liters and then add this converted amount to 8.24 liters.

• First, we convert 160 milliliters to liters. Knowing that $1 \text{ liter} = 1000 \text{ milliliters}$, we perform the calculation:
$\frac{160 \text{ ml}}{1000} = 0.16 \text{ liters}$
• Next, we add the converted volume to the initial 8.24 liters:
$\text{Total volume in liters} = 8.24 \text{ liters} + 0.16 \text{ liters}$
• This gives us:
$\text{Total volume} = 8.40 \text{ liters}$

Thus, the final volume is $8.4 \, \text{liters}$.

Therefore, the solution to the problem is $8.4 \, \text{l}$, which matches choice 2.

To solve this problem, we need to convert the volume $2\frac{3}{6} \, m^3$ to cubic decimeters.

• Step 1: Convert the fractional volume to a decimal. $2\frac{3}{6} \, m^3 = 2.5 \, m^3$.
• Step 2: Use the conversion factor $1 \, m^3 = 1000 \, dm^3$.
• Step 3: Multiply 2.5 by 1000 to change the unit from cubic meters to cubic decimeters.

Calculation:

$2.5 \, m^3 \times 1000 \, dm^3/m^3 = 2500 \, dm^3$

Therefore, the volume of $2\frac{3}{6} \, m^3$ is equivalent to $\mathbf{2500 \, dm^3}$.