Calculate Volume: Finding Total Space of 3 Identical 130 m³ Cuboids

Q: Why do I need to convert from m³ to cm³?

The answer choices are given in cubic centimeters (cm³), not cubic meters. You must convert your final answer to match the required units in the options.

Q: How do I remember the conversion factor for cubic units?

Remember: $ 1 \, m = 100 \, cm $, so $ 1 \, m^3 = 100 \times 100 \times 100 = 1,000,000 \, cm^3 $. Think of it as cubing the linear conversion!

Q: Can I just multiply 130 by 3 to get the answer?

That's only the first step! You get 390 m³, but the answer choices need cm³. You must then multiply by 1,000,000 to convert units properly.

Q: What if I calculated 130 × 3 × 1,000,000 all at once?

That works too! $ 130 \times 3 \times 1,000,000 = 390,000,000 \, cm^3 $. Just make sure you understand why each step is needed.

Volume Multiplication with Unit Conversion

The volume of a cuboid is equal to 130 cubic meters.

What is the volume of 3 such cubes of the same size, given in m³?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the volume of three boxes in cubic centimeters.

00:14 First, multiply the volume of one box by three, to get the volume of all three boxes.

00:20 Now, since this volume is in cubic meters, let's convert it to cubic centimeters.

00:27 To make this conversion, multiply the result by one million.

00:35 Alright, let's do the calculation together.

00:42 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The volume of a cuboid is equal to 130 cubic meters.

What is the volume of 3 such cubes of the same size, given in m³?

Step-by-step solution

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

Step 1: Calculate the total volume of 3 cuboids in cubic meters.
Step 2: Convert this volume from cubic meters to cubic centimeters.

Let's go through each step:

Step 1: The volume of one cuboid is given as $130 \, m^3$ . Since we need the volume of 3 such cuboids, we multiply:

$3 \times 130 \, m^3 = 390 \, m^3$

Step 2: To convert cubic meters to cubic centimeters, we use the conversion factor: $1 \, m^3 = 1,000,000 \, cm^3$ . Therefore,

$390 \, m^3 = 390 \times 1,000,000 \, cm^3 = 390,000,000 \, cm^3$ .

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

Final Answer

$390,000,000cm^3$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply volume by number of identical objects for total volume
Technique: Convert cubic meters using $1 \, m^3 = 1,000,000 \, cm^3$
Check: Verify units match answer options: 390 m³ becomes 390,000,000 cm³ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert units or using wrong conversion factor
Don't calculate 3 × 130 = 390 and stop there = wrong units! The answer choices are in cm³, not m³. Always convert 390 m³ to cubic centimeters using 1 m³ = 1,000,000 cm³.

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 do I need to convert from m³ to cm³?

The answer choices are given in cubic centimeters (cm³), not cubic meters. You must convert your final answer to match the required units in the options.

How do I remember the conversion factor for cubic units?

Remember: $1 \, m = 100 \, cm$ , so $1 \, m^3 = 100 \times 100 \times 100 = 1,000,000 \, cm^3$ . Think of it as cubing the linear conversion!

Can I just multiply 130 by 3 to get the answer?

That's only the first step! You get 390 m³, but the answer choices need cm³. You must then multiply by 1,000,000 to convert units properly.

What if I calculated 130 × 3 × 1,000,000 all at once?

That works too! $130 \times 3 \times 1,000,000 = 390,000,000 \, cm^3$ . Just make sure you understand why each step is needed.

Why does the question mention 'cubes' but talk about 'cuboids'?

The problem uses both terms, but they mean the same thing here - rectangular 3D shapes. The volume calculation method is identical for both.

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