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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143535 milliliters are? liters

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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