Calculate Volume of Rectangular Prism: 8×3×2 Units Problem

Q: Why do I need to multiply all three numbers?

A rectangular prism is three-dimensional, so you need all three measurements! Length and width give you the base area, but you must multiply by height to fill the entire space.

Q: What's the difference between area and volume?

Area measures flat surfaces (2D) using two dimensions. Volume measures space inside (3D) using three dimensions. That's why volume needs length × width × height!

Q: Does the order of multiplication matter?

No! You can multiply $ 3 \times 8 \times 2 $ in any order and get the same answer: 3 × 8 × 2 = 8 × 3 × 2 = 2 × 8 × 3 = 48.

Q: How can I visualize this to check my answer?

Imagine stacking unit cubes to fill the prism. You'd have 3 rows × 8 columns × 2 layers = 48 total cubes, confirming your volume calculation!

Q: What units should my answer have?

Volume uses cubic units! If dimensions are in centimeters, the volume is in cubic centimeters (cm³). Always include the proper cubic units in your final answer.

Volume Formula with Three-Dimensional Measurements

Calculate the volume of the rectangular prism below using the data provided.

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Step-by-step written solution

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Understand the problem

Calculate the volume of the rectangular prism below using the data provided.

Step-by-step solution

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

Identify the given dimensions of the rectangular prism.
Use the formula for volume: $V = l \times w \times h$ .
Calculate the volume by plugging in the given values.

Now, let's work through each step:
Step 1: The problem provides the dimensions of the prism: length = 3, width = 8, height = 2.
Step 2: Applying the formula, we have $V = l \times w \times h = 3 \times 8 \times 2$ .
Step 3: Performing the multiplication, we obtain $V = 3 \times 8 \times 2 = 24 \times 2 = 48$ .

Therefore, the volume of the rectangular prism is $48$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of rectangular prism equals length times width times height
Technique: Multiply all three dimensions: $3 \times 8 \times 2 = 48$
Check: Count unit cubes or verify formula gives same result ✓

Common Mistakes

Avoid these frequent errors

Multiplying only two dimensions instead of all three
Don't calculate $3 \times 8 = 24$ and stop there = missing the third dimension! This gives area instead of volume. Always multiply all three measurements: 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.

FAQ

Everything you need to know about this question

Why do I need to multiply all three numbers?

A rectangular prism is three-dimensional, so you need all three measurements! Length and width give you the base area, but you must multiply by height to fill the entire space.

What's the difference between area and volume?

Area measures flat surfaces (2D) using two dimensions. Volume measures space inside (3D) using three dimensions. That's why volume needs length × width × height!

Does the order of multiplication matter?

No! You can multiply $3 \times 8 \times 2$ in any order and get the same answer: 3 × 8 × 2 = 8 × 3 × 2 = 2 × 8 × 3 = 48.

How can I visualize this to check my answer?

Imagine stacking unit cubes to fill the prism. You'd have 3 rows × 8 columns × 2 layers = 48 total cubes, confirming your volume calculation!

What units should my answer have?

Volume uses cubic units! If dimensions are in centimeters, the volume is in cubic centimeters (cm³). Always include the proper cubic units in your final answer.

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