Volume Exploration Worksheet

Name:

Date:

📘 Part 1: Understanding Volume

1. Which sentence best describes volume?

The amount of 2-dimensional space inside a shape.

The total amount of 3-dimensional space inside an object.

The distance around a solid object.

2. Which of the following are needed to calculate the volume of a rectangular prism? (Check all that apply)

Length (l)

Width (w)

Depth / Height (d or h)

Circumference

3. Map the process you use to find the volume of a rectangular prism. Write the steps in order (short answers).

4. Sketch a rectangular prism. Label the length (l), width (w) and depth (d). Show the base and indicate which measurement you will multiply first.

✏️ Part 2: Compute Volumes (You Do)

5. Find the volume. Show your working. Units: cubic centimetres (cm³).

Prism A: l = 8 cm, w = 5 cm, d = 4 cm

6. Find the volume. Show your working. Units: cm³.

Prism B: l = 7 cm, w = 6 cm, d = 3 cm

7. Find the volume. Show your working. Units: cm³.

Prism C: l = 9 cm, w = 2 cm, d = 5 cm

8. Compare the three volumes above. Which prism has the greatest volume? Explain in one sentence using numbers.

📊 Part 3: Real-World Statistical Comparisons (z-scores)

9. The class measured small storage boxes. The class distribution has mean volume = 100 cm³ and standard deviation = 15 cm³ (given). Two students measured boxes:

Student A: 130 cm³ Student B: 115 cm³

a) Calculate the z-score for Student A and Student B. (Show the formula and working.)

b) Which student's box is more unusual compared to the class? Explain using the z-scores (one sentence).

10. Real packing question: My small Astra wagon boot has about 1600 cm³ of useful space for smaller boxes (story context). If you have four identical boxes of volume 400 cm³ each, will they all fit? Show a short calculation and answer Yes or No.

Instructional notes (for teacher):

Differentiation strategies: Provide a step-by-step worksheet copy with labelled diagrams for learners who need extra support. Allow peers to verbalise the mapping process first; provide manipulatives (small cubes) for hands-on measurement. Offer one-to-one guidance for z-score interpretation using simple examples.

Extension activities: Ask advanced learners to collect five box volumes from home, calculate mean and standard deviation, compute z-scores for each box and write a short paragraph comparing which boxes would be most efficient for packing the car boot. Challenge: convert a volume in cm³ to litres (1000 cm³ = 1 L) and compare with petrol can capacities in litres.