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Volume and Composite Shapes

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Volume and Composite Shapes

Volume and Composite Shapes

3D shapes and volume illustration

📐 Part 1: Volume of Rectangular Prisms

1. Calculate the volume of a rectangular prism with the following dimensions:

Length = 8 cm, Width = 5 cm, Height = 3 cm

Formula: Volume = length × width × height

Volume = _______ cm³

2. A storage box measures 12 cm long, 7 cm wide, and 4 cm high. What is its volume?

Volume = _______ cm³

3. Circle the correct formula for finding the volume of a rectangular prism:

Volume = length + width + height

Volume = length × width × height

Volume = length × width ÷ height

Volume = 2 × (length + width + height)

🔺 Part 2: Volume of Triangular Prisms

4. For a triangular prism, the volume formula is:

Volume = (Area of triangular base) × height

Where Area of triangle = (base × height) ÷ 2

5. Calculate the volume of a triangular prism where:

Triangle base = 6 cm, Triangle height = 4 cm, Prism length = 10 cm

Step 1: Area of triangular base = ________________

Step 2: Volume = Area × length = ________________

Volume = _______ cm³

6. Which of these are correct units for measuring volume? (Check all that apply)

cm³ (cubic centimetres)

cm² (square centimetres)

m³ (cubic metres)

litres

metres

🏗️ Part 3: Composite Shapes

7. A composite shape is made by combining two or more simple shapes. To find the total volume, you _______ the volumes of each part.

subtract

add

multiply

divide

8. A composite shape is made from two rectangular prisms:

Prism A: 5 cm × 3 cm × 2 cm

Prism B: 4 cm × 2 cm × 3 cm

Calculate the total volume:

Volume of Prism A = _______ cm³

Volume of Prism B = _______ cm³

Total Volume = _______ cm³

9. Draw a composite shape made from two rectangular prisms and label the dimensions:

📏 Part 4: Practical Measuring

10. When measuring 3D shapes to find volume, which tools would be most useful? (Check all that apply)

Ruler or measuring tape

Protractor

Centicubes

Calculator

Compass

11. Match the measurement method with its description:
1. Counting unit cubes
2. Using a formula
3. Measuring dimensions
A. Using length × width × height
B. Finding length, width, height with ruler
C. Building with centicubes and counting
12. Explain why it's important to use the same units (like centimetres) when measuring all dimensions of a shape:

🧠 Part 5: Problem Solving

13. A swimming pool is shaped like a rectangular prism. It is 25 metres long, 10 metres wide, and 2 metres deep. What is the volume of water it can hold?

Volume = _______ m³

14. Design your own composite shape problem:

Create a composite shape using at least two prisms. Draw it below and write the dimensions:

Describe your shape: _________________________________________________

Calculate the total volume and show your working:

15. True or False: Circle your answers

a) Volume is measured in square units. True / False

b) A composite shape's volume equals the sum of its parts. True / False

c) All prisms have the same volume formula. True / False

d) 1000 cm³ = 1 litre. True / False

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