Calculate Cuboid Volume: Finding Space in an 8×5×12 Rectangular Prism

Cuboid Volume with Rectangular Dimensions

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the volume of the box
00:03 We'll use the formula for calculating box volume
00:07 Width multiplied by Height multiplied by Length
00:12 Substitute appropriate values into the formula according to the given data and solve for the volume
00:46 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

2

Step-by-step solution

To determine the volume of a cuboid, we apply the formula:

  • Step 1: Identify the dimensions of the cuboid:
    • Length (l l ) = 12 cm
    • Width (w w ) = 8 cm
    • Height (h h ) = 5 cm
  • Step 2: Apply the volume formula for a cuboid:

The formula to find the volume (V V ) of a cuboid is:

V=l×w×h V = l \times w \times h

Step 3: Substitute the given dimensions into the formula and calculate: V=12×8×5 V = 12 \times 8 \times 5

Step 4: Perform the multiplication in stages for clarity:

First, calculate 12×8=96 12 \times 8 = 96

Then multiply the result by 5: 96×5=480 96 \times 5 = 480

Therefore, the volume of the cuboid is 480cm3\mathbf{480 \, \text{cm}^3}.

3

Final Answer

480 cm³

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume = length × width × height for all cuboids
  • Technique: Calculate step-by-step: 12 × 8 = 96, then 96 × 5 = 480
  • Check: Units must be cubic (cm³) and answer should be reasonable ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 12 + 8 + 5 = 25 cm³! This gives you perimeter thinking, not volume. Volume measures 3D space inside the cuboid. Always multiply all three dimensions: length × width × height.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

121212888555

FAQ

Everything you need to know about this question

Why do we multiply all three dimensions instead of adding them?

+

Volume measures the space inside a 3D shape. Think of it like stacking unit cubes - you need length × width × height layers. Adding would give you the total of the edges, not the space!

Does it matter which dimension I call length, width, or height?

+

No! Multiplication is commutative, so 12 × 8 × 5 = 8 × 12 × 5 = 5 × 8 × 12. The volume will always be the same regardless of order.

What if I forget to include the cubic units (cm³)?

+

Always include cubic units for volume! Since you're multiplying three lengths (cm × cm × cm), the result must be cm³. Without units, your answer is incomplete.

How can I remember the volume formula?

+

Think of filling a box with unit cubes. You need to know how many cubes fit along each direction, then multiply to find the total: V=l×w×h V = l \times w \times h

What's the difference between a cuboid and a cube?

+

A cube has all sides equal, while a cuboid can have different dimensions. Both use the same volume formula, but a cube would be V=s3 V = s^3 where s is the side length.

Is 480 cm³ a reasonable answer for this cuboid?

+

Yes! The cuboid is fairly large (12×8×5 cm), so 480 cm³ makes sense. That's about half a liter of space, which matches the size shown in the diagram.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Cuboids questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations