Volume of 3D Shapes

Name:

Date:

3D shapes including cube, rectangular prism, and cylinder

📐 Part 1: Volume Formulae and Calculations

WALT: Calculate the volume of cubes, rectangular prisms, and cylinders using appropriate formulae.

Remember: Volume = the amount of space inside a 3D shape (measured in cubic units like cm³ or m³)

1. Calculate the volume of a cube with side length 4 cm.

Formula: V = side³

Volume = _______ cm³

2. Find the volume of a rectangular prism with length 6 m, width 3 m, and height 2 m.

Formula: V = length × width × height

Volume = _______ m³

3. Calculate the volume of a cylinder with radius 5 cm and height 8 cm. (Use π = 3.14)

Formula: V = π × radius² × height

Volume = _______ cm³

4. Which shape has the greatest volume?

A cube with side 3 m

A rectangular prism 2m × 4m × 3m

A cylinder with radius 2m and height 4m (π = 3.14)

🧠 Part 2: Problem Solving

5. A swimming pool is shaped like a rectangular prism. It is 25 metres long, 10 metres wide, and 2 metres deep. How many cubic metres of water does it hold when full?

Answer: _______ m³

6. A cylindrical water tank has a radius of 3 metres and a height of 5 metres. Calculate its volume in cubic metres. (Use π = 3.14)

Answer: _______ m³

7. True or False: If you double all the dimensions of a cube, its volume increases by 8 times.

True

False

Explain your reasoning:

⭐ Part 3: Extension Challenge

8. Advanced: A composite shape is made by placing a cylinder on top of a rectangular prism. The prism has dimensions 4m × 4m × 2m, and the cylinder has radius 2m and height 3m. Calculate the total volume.

Total volume = _______ m³

9. Investigation: A cube and a cylinder have the same volume of 64 cm³. If the cube has side length 4 cm, what is the relationship between the cylinder's radius and height? Describe your findings.

10. Success Criteria Check: Tick the boxes for what you can now do confidently:

Explain what volume means

Calculate volume of cubes using V = side³

Calculate volume of rectangular prisms using V = l × w × h

Calculate volume of cylinders using V = π × r² × h

Use correct cubic units (cm³, m³)

Solve real-world volume problems