Volume Conversion: Convert 390 m³ Cube to cm³

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

Since we're converting cubic units, we need to cube the linear conversion. $ 1 \, \text{m} = 100 \, \text{cm} $, so $ 1 \, \text{m}^3 = (100 \, \text{cm})^3 = 1,000,000 \, \text{cm}^3 $!

Q: How do I remember which direction to multiply or divide?

Going from larger to smaller units means the number gets bigger! From m³ to cm³, you're going smaller, so multiply by 1,000,000 to get more cubic centimeters.

Q: What if I need to convert from cm³ to m³?

For the reverse conversion, divide by 1,000,000. Example: $ 5,000,000 \, \text{cm}^3 ÷ 1,000,000 = 5 \, \text{m}^3 $.

Q: Is there an easier way to handle all those zeros?

Yes! Use scientific notation: $ 390 \times 10^6 = 3.9 \times 10^8 \, \text{cm}^3 $. This helps avoid counting errors with large numbers.

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

Absolutely! For any cubic conversion, cube the linear factor. Example: $ 1 \, \text{ft}^3 = (12 \, \text{in})^3 = 1,728 \, \text{in}^3 $.

Volume Conversion with Cubic Units

If the volume of a cube is 390 m³, then what is its volume in cm³?

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Understand the problem

If the volume of a cube is 390 m³, then what is its volume in cm³?

Step-by-step solution

To convert the volume from cubic meters to cubic centimeters, we use the conversion factor:

$1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3$ .

Thus, we need to perform the following calculation:

$390 \, \text{m}^3 \times 1,000,000 \, \text{cm}^3/\text{m}^3 = 390,000,000 \, \text{cm}^3$ .

Therefore, the volume of the cube in cubic centimeters is $390,000,000 \, \text{cm}^3$ .

Final Answer

$390,000,000cm^3$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: $1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3$ for cubic volume units
Technique: Multiply given volume by 1,000,000: $390 \times 1,000,000 = 390,000,000$
Check: Count zeros carefully: 390 m³ becomes 390,000,000 cm³ (6 added zeros) ✓

Common Mistakes

Avoid these frequent errors

Using linear conversion factor for cubic units
Don't multiply by 100 (m to cm linear conversion) = 39,000 cm³! Cubic units require the conversion factor cubed: 100³ = 1,000,000. Always cube the linear conversion factor for volume units.

Practice Quiz

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How many cm³ are there in a m³?

FAQ

Everything you need to know about this question

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

Since we're converting cubic units, we need to cube the linear conversion. $1 \, \text{m} = 100 \, \text{cm}$ , so $1 \, \text{m}^3 = (100 \, \text{cm})^3 = 1,000,000 \, \text{cm}^3$ !

How do I remember which direction to multiply or divide?

Going from larger to smaller units means the number gets bigger! From m³ to cm³, you're going smaller, so multiply by 1,000,000 to get more cubic centimeters.

What if I need to convert from cm³ to m³?

For the reverse conversion, divide by 1,000,000. Example: $5,000,000 \, \text{cm}^3 ÷ 1,000,000 = 5 \, \text{m}^3$ .

Is there an easier way to handle all those zeros?

Yes! Use scientific notation: $390 \times 10^6 = 3.9 \times 10^8 \, \text{cm}^3$ . This helps avoid counting errors with large numbers.

Do I use the same method for other cubic conversions?

Absolutely! For any cubic conversion, cube the linear factor. Example: $1 \, \text{ft}^3 = (12 \, \text{in})^3 = 1,728 \, \text{in}^3$ .

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