Calculate Cuboid Volume: Finding V = 8cm × 10cm × 9cm

Cuboid Volume with Three-Dimensional Multiplication

Given the cuboid whose height is equal to 9 cm

Length is equal to 8 cm

Width is equal to 10 cm

Find the volume of the cuboid

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's find the volume of the box!
00:14 We'll use a formula to calculate the box's volume.
00:18 We'll substitute the given values into the formula and solve it step by step, to find the volume.
00:37 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the cuboid whose height is equal to 9 cm

Length is equal to 8 cm

Width is equal to 10 cm

Find the volume of the cuboid

2

Step-by-step solution

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

  • Step 1: Identify the given dimensions: length, width, and height.
  • Step 2: Apply the volume formula for a cuboid.
  • Step 3: Perform the multiplication to find the volume.
  • Step 4: Match the result with the provided choices to confirm the correct answer.

Now, let's work through each step:
Step 1: We are given the cuboid's dimensions: length = 8 cm, width = 10 cm, height = 9 cm.
Step 2: To find the volume V V of the cuboid, we use the formula:
V=length×width×height V = \text{length} \times \text{width} \times \text{height} .
Step 3: Substitute the given values into the formula:
V=8cm×10cm×9cm V = 8 \, \text{cm} \times 10 \, \text{cm} \times 9 \, \text{cm} .
Calculate the product:
V=8×10×9=720cm3 V = 8 \times 10 \times 9 = 720 \, \text{cm}^3 .
Step 4: The calculated volume is 720cm3 720 \, \text{cm}^3 , which matches choice 4.

Therefore, the solution to the problem is 720cm3 720 \, \text{cm}^3 .

3

Final Answer

720 720

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume equals length times width times height
  • Technique: Multiply step-by-step: 8 × 10 = 80, then 80 × 9 = 720
  • Check: Units should be cubic (cm³) and result matches given choices ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 8 + 10 + 9 = 27 cm! This gives perimeter-like thinking, not volume. Volume measures space inside, which requires multiplying all three dimensions. Always multiply length × width × height for volume.

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?

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Volume measures space inside a 3D shape! Think of it as layers: you have 8 × 10 = 80 square cm per layer, and you stack 9 layers high, giving 80 × 9 = 720 cubic cm total.

Does the order of multiplication matter?

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No! You can multiply length × width × height in any order due to the commutative property. Whether you do 8 × 10 × 9 or 9 × 8 × 10, you'll get 720 cm³.

What's the difference between cm² and cm³?

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cm² measures flat area (like a square), while cm³ measures volume (space inside a box). Always use cubic units for volume!

How can I remember the volume formula?

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Think "How much stuff fits inside?" You need to know how long, how wide, and how tall the container is. Multiply all three to find the total space: V = L × W × H.

What if I get a different answer choice?

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  • Double-check your multiplication: 8 × 10 = 80, then 80 × 9 = 720
  • Make sure you didn't add: 8 + 10 + 9 = 27 (wrong!)
  • Verify units: Should be cm³, not cm

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