Convert 100 m³ to cm³: Metric Volume Conversion Problem

Q: Why do I need to cube the conversion factor?

Because volume is three-dimensional! When converting linear units like meters to centimeters, you multiply by 100. But for volume, you're converting length × width × height, so you need $ 100 \times 100 \times 100 = 100^3 $.

Q: How do I remember that 1 m³ equals 1,000,000 cm³?

Think of it step by step: 1 meter = 100 centimeters, so $ 1 \text{ m}^3 = (100 \text{ cm})^3 = 100^3 = 1,000,000 \text{ cm}^3 $. It's six zeros because $ 10^2 \times 10^2 \times 10^2 = 10^6 $!

Q: What if I'm converting the other way, from cm³ to m³?

Then you divide by 1,000,000 instead of multiply! For example: 5,000,000 cm³ = 5,000,000 ÷ 1,000,000 = 5 m³.

Q: Do I use the same method for other volume conversions?

Yes! Always cube the linear conversion factor. For example: 1 ft = 12 in, so 1 ft³ = $ 12^3 = 1,728 $ in³.

Q: Why is the answer so much bigger than the original number?

Cubic centimeters are much smaller than cubic meters, so you need many more of them! Think about how many sugar cubes (cm³) would fit in a refrigerator box (m³) - millions!

Unit Conversion with Cubic Measurements

What is 100 m³ written as cm³?

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Understand the problem

What is 100 m³ written as cm³?

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

Final Answer

$100,000,000cm^3$

Key Points to Remember

Essential concepts to master this topic

Rule: Cube the linear conversion factor for volume units
Technique: Since 1 m = 100 cm, then 1 m³ = (100)³ = 1,000,000 cm³
Check: Verify dimensions match: m³ converts to cm³, both are volume units ✓

Common Mistakes

Avoid these frequent errors

Using the linear conversion factor instead of cubing it
Don't just multiply 100 m³ by 100 to get 10,000 cm³ = wrong by factor of 10,000! This treats volume like length conversion. Always cube the linear conversion factor: 100 × (100)³ = 100 × 1,000,000.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to cube the conversion factor?

Because volume is three-dimensional! When converting linear units like meters to centimeters, you multiply by 100. But for volume, you're converting length × width × height, so you need $100 \times 100 \times 100 = 100^3$ .

How do I remember that 1 m³ equals 1,000,000 cm³?

Think of it step by step: 1 meter = 100 centimeters, so $1 \text{ m}^3 = (100 \text{ cm})^3 = 100^3 = 1,000,000 \text{ cm}^3$ . It's six zeros because $10^2 \times 10^2 \times 10^2 = 10^6$ !

What if I'm converting the other way, from cm³ to m³?

Then you divide by 1,000,000 instead of multiply! For example: 5,000,000 cm³ = 5,000,000 ÷ 1,000,000 = 5 m³.

Do I use the same method for other volume conversions?

Yes! Always cube the linear conversion factor. For example: 1 ft = 12 in, so 1 ft³ = $12^3 = 1,728$ in³.

Why is the answer so much bigger than the original number?

Cubic centimeters are much smaller than cubic meters, so you need many more of them! Think about how many sugar cubes (cm³) would fit in a refrigerator box (m³) - millions!

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