Convert 35.3 cm³ to m³: Cubic Volume Transformation

Unit Conversion with Volume Cubes

35.3 cm³ are? m³

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1

Understand the problem

35.3 cm³ are? m³

2

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 35.3cm3 35.3 \, \text{cm}^3 .
  • Step 2: Use the conversion factor between cubic centimeters and cubic meters. We know that 1m3=1,000,000cm3 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:

35.3cm31,000,000=35.31,000,000m3\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 35.31,000,000m3\frac{35.3}{1,000,000} \, \text{m}^3.

Thus, the correct answer is:

35.31,000,000m3\frac{35.3}{1,000,000} \, \text{m}^3

From the given choices, the correct choice is:

35.31,000,000m3 \frac{35.3}{1,000,000m^3}

3

Final Answer

35.31,000,000m3 \frac{35.3}{1,000,000m^3}

Key Points to Remember

Essential concepts to master this topic
  • Conversion Factor: One cubic meter equals one million cubic centimeters
  • Technique: Divide by 1,000,000: 35.31,000,000=0.0000353 m3 \frac{35.3}{1,000,000} = 0.0000353 \text{ m}^3
  • Check: Multiply result by 1,000,000 to get back 35.3 cm³ ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong conversion factor for cubic units
    Don't multiply or divide by just 100 like with length conversions = wrong answer! Volume involves three dimensions, so 1 m³ = 100³ = 1,000,000 cm³. Always use 1,000,000 as the conversion factor for cubic units.

Practice Quiz

Test your knowledge with interactive questions

Convert \( 16,848dm^3 \) into liters.

FAQ

Everything you need to know about this question

Why is the conversion factor 1,000,000 instead of 100?

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Because volume is three-dimensional! Since 1 m = 100 cm, we have 1 m³ = (100 cm)³ = 100 × 100 × 100 = 1,000,000 cm³. Each dimension gets multiplied!

Should I memorize all these conversion factors?

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Focus on understanding the pattern! For length: ×100, for area: ×10,000, for volume: ×1,000,000. Each adds two more zeros because you're adding another dimension.

Why is my answer so small?

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That's normal! A cubic meter is huge compared to a cubic centimeter. Think of it this way: 35.3 cm³ is like a small ice cube, while 1 m³ could hold 1000 liters!

Can I write the answer as a decimal instead of a fraction?

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Yes! 35.31,000,000=0.0000353 m3 \frac{35.3}{1,000,000} = 0.0000353 \text{ m}^3 . Both forms are correct, but the fraction shows the conversion process more clearly.

How do I remember which way to multiply or divide?

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Think about size: cm³ are smaller units, so you need many of them to make 1 m³. Going from small to big units means dividing by a large number!

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