Volume Units Practice Problems with Solutions | Math Practice

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 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 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 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 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 $143.535l$.