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Composite Area Volume Problems
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Composite Area Volume Problems
📐 Part 1: Composite Shape Area Problems
1. A garden bed is made up of a rectangle (8m × 5m) with a semicircle attached to one end (diameter 5m). Calculate the total area of the garden bed.
2. A sports field consists of a rectangular centre section (60m × 40m) with a quarter circle at each corner (radius 10m). What is the total area?
3. Which strategy is most efficient for finding the area of a composite shape?
Always break it into the smallest possible pieces
Look for the largest recognisable shapes first
Use subtraction when shapes overlap
Both B and C are correct
4. A concrete path surrounds a circular fountain. The outer edge forms a circle with radius 8m, and the fountain has radius 3m. Calculate the area of the path.
📦 Part 2: Volume Problems and Investigation
5. A storage container is shaped like a rectangular prism (4m × 3m × 2.5m) with a triangular prism section on top (same base, height 1.5m). Find the total volume.
6. Investigation: A pyramid and a rectangular prism have the same base area (25 square metres) and height (6 metres). If the prism's volume is 150 cubic metres, predict the pyramid's volume and explain your reasoning.
7. A water tank consists of a cylindrical base (radius 2m, height 3m) topped with a hemisphere (radius 2m). Calculate the total volume.
8. Which of these volume relationships are correct? (Select all that apply)
Pyramid volume = ⅓ × base area × height
Cylinder volume = π × radius² × height
Sphere volume = ⅔ × π × radius³
Triangular prism volume = ½ × base × height × length
✍️ Part 3: Problem-Solving Explanation
9. A swimming pool has a rectangular main section (20m × 10m × 2m deep) and a circular spa attached (diameter 6m, same depth). Explain step-by-step how you would calculate the total volume of water needed to fill both sections.
10. Create your own composite shape problem involving at least two different shapes. Include the solution and explain why you chose to decompose it the way you did.
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