Convert 31m³ to Litres: Step-by-Step Volume Conversion

Q: Why is 1 cubic meter equal to 1000 litres?

A cubic meter is $ 1m \times 1m \times 1m $. Since 1 meter = 100 centimeters, this becomes $ 100cm \times 100cm \times 100cm = 1,000,000 cm^3 $. And since 1 litre = 1000 cm³, we get 1000 litres!

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

Think about size: Cubic meters are much bigger than litres, so when converting m³ to litres, you should get a larger number. This means multiply, not divide!

Q: What if I need to convert litres back to cubic meters?

Then you do the opposite: divide by 1000. For example, $ 5000l ÷ 1000 = 5m^3 $. Remember: bigger units = smaller numbers!

Q: Are there any other volume units I should know?

Millilitres: 1 litre = 1000 mlCubic centimeters: 1 litre = 1000 cm³Cubic decimeters: 1 litre = 1 dm³

Q: Can I use this method for any volume conversion?

Yes! The key is knowing your conversion factors. Always set up the multiplication so unwanted units cancel out, leaving you with the units you want.

Volume Conversion with Cubic Meter Units

Convert $31m^3$ into litres.

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Understand the problem

Convert $31m^3$ into litres.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the conversion factor.
Step 2: Apply the conversion factor to the given volume in cubic meters.
Step 3: Calculate the corresponding volume in liters.

Now, let's work through each step:

Step 1: We know that $1 \, m^3$ is equivalent to $1000 \, l$ .

Step 2: We have a volume of $31 \, m^3$ . To convert this to liters, we multiply the given volume by the conversion factor:

$31 \, m^3 \times 1000 \, \frac{l}{m^3} = 31000 \, l$ .

Step 3: Hence, the volume of $31 \, m^3$ is $31000 \, l$ .

Therefore, the solution to the problem is $31000 \, l$ .

Final Answer

$31000l$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: One cubic meter equals exactly 1000 litres
Technique: Multiply volume by 1000: $31 \times 1000 = 31000$
Check: Verify units cancel correctly: $m^3 \times \frac{l}{m^3} = l$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the conversion factor direction
Don't divide by 1000 when converting m³ to litres = tiny wrong answer! This gives 0.031l instead of 31000l because you're going backwards. Always multiply by 1000 when converting from larger units (m³) to smaller units (litres).

Practice Quiz

Test your knowledge with interactive questions

How many cm³ are there in a m³?

FAQ

Everything you need to know about this question

Why is 1 cubic meter equal to 1000 litres?

A cubic meter is $1m \times 1m \times 1m$ . Since 1 meter = 100 centimeters, this becomes $100cm \times 100cm \times 100cm = 1,000,000 cm^3$ . And since 1 litre = 1000 cm³, we get 1000 litres!

How do I remember which way to multiply or divide?

Think about size: Cubic meters are much bigger than litres, so when converting m³ to litres, you should get a larger number. This means multiply, not divide!

What if I need to convert litres back to cubic meters?

Then you do the opposite: divide by 1000. For example, $5000l ÷ 1000 = 5m^3$ . Remember: bigger units = smaller numbers!

Are there any other volume units I should know?

Millilitres: 1 litre = 1000 ml
Cubic centimeters: 1 litre = 1000 cm³
Cubic decimeters: 1 litre = 1 dm³

Can I use this method for any volume conversion?

Yes! The key is knowing your conversion factors. Always set up the multiplication so unwanted units cancel out, leaving you with the units you want.

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