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Lesson 4-4

Rectangular Prism Volume

Understand volume concepts and calculate volumes of rectangular prisms. Master volume through box packing challenges and real-world applications.

Learning Scenario: Box Packing Challenge

Scenario: You're packing boxes for shipping! You have a rectangular box that's 4cm long, 3cm wide, and 2cm tall. You need to figure out how many 1cm³ unit cubes can fit inside. Then you need to compare different boxes: one that's 6cm × 2cm × 2cm and another that's 3cm × 3cm × 3cm. Which box can hold more cubes?

This challenge will teach you about volume - the amount of space inside a 3D shape. You'll learn to calculate volume using the formula and understand what volume means in real life!

What is Volume?

Volume is the amount of space inside a 3D shape. It's measured in cubic units like cm³, m³, or ft³.

Think of it as:

  • • How many unit cubes fit inside
  • • The amount of liquid a container holds
  • • The space an object takes up
  • • 3D space measurement
Volume Formula

For rectangular prisms, volume = length × width × height

Formula:

V = l × w × h

Units: cm³, m³, ft³, etc.

Step-by-Step Learning
1

Understanding Unit Cubes

A unit cube is a cube with sides of 1 unit. Volume tells us how many unit cubes fit inside a shape.

Example: A 4cm × 3cm × 2cm box can fit 4 × 3 × 2 = 24 unit cubes

2

Using the Volume Formula

Multiply length × width × height to find volume. Make sure all measurements are in the same units.

Example: 6cm × 2cm × 2cm = 24cm³

3

Comparing Volumes

To compare volumes, calculate each one and see which is larger. The larger volume can hold more.

Example: 24cm³ vs 27cm³ (3×3×3) → 27cm³ is larger

Interactive Activities

Activity 1: Unit Cube Counting

Count unit cubes in these boxes:

  • • Box 1: 3cm × 2cm × 2cm
  • • Box 2: 4cm × 3cm × 1cm
  • • Box 3: 2cm × 2cm × 3cm
  • • Box 4: 5cm × 2cm × 2cm
  • • Box 5: 3cm × 3cm × 2cm

Activity 2: Volume Comparison

Compare these volumes:

  • • 6cm × 2cm × 2cm vs 4cm × 3cm × 2cm
  • • 3cm × 3cm × 3cm vs 5cm × 2cm × 2cm
  • • 8cm × 1cm × 2cm vs 4cm × 2cm × 2cm
  • • 2cm × 2cm × 4cm vs 3cm × 2cm × 3cm
Practice Problems

Problem Set 1: Basic Volume

1. Box: 4cm × 3cm × 2cm. Volume?

2. Box: 5cm × 2cm × 3cm. Volume?

3. Box: 6cm × 4cm × 1cm. Volume?

4. Box: 3cm × 3cm × 3cm. Volume?

Problem Set 2: Volume Comparison

5. Which is larger: 4×3×2 or 3×3×3?

6. Which is larger: 6×2×2 or 4×3×2?

7. Which is larger: 5×2×3 or 3×4×2?

8. Which is larger: 8×1×2 or 4×2×2?

Problem Set 3: Real-World Applications

9. Shipping box: 10cm × 8cm × 6cm. Volume?

10. Storage container: 12cm × 10cm × 5cm. Volume?

11. Aquarium: 20cm × 15cm × 10cm. Volume?

12. Gift box: 8cm × 8cm × 8cm. Volume?

Common Mistakes to Avoid

❌ Confusing volume with area

Wrong: Using length × width only (that's area)

Correct: Volume = length × width × height (3D measurement)

❌ Using different units

Wrong: 4cm × 3m × 2cm (mixed units)

Correct: Convert all measurements to the same unit first

Key Takeaways

Volume measures the space inside a 3D shape

Volume = length × width × height for rectangular prisms

Volume is measured in cubic units (cm³, m³, ft³)

Always use the same units for all measurements