Real-World Measurement Problems

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📐 Part 1: Composite Shape Problems (Show full workings)

Instructions: For each question state the formula you use and justify why it applies. Show step-by-step workings and give a final answer with units. Write clearly in the space provided.

1. A rectangular lawn is 12.0 m by 8.0 m. A uniform path 1.5 m wide runs around the lawn. Calculate:

a) the area of the path (m²).

2. A backyard pool is made from a rectangle 8.0 m long and 4.0 m wide with a semicircular end attached to one short side (the semicircle has radius 2.0 m). Find:

a) the area of the water surface (m²). b) the length of the pool edge around the water (perimeter of the composite shape, m).

3. A glass fish tank has internal dimensions 1.20 m long × 0.50 m wide × 0.60 m high. The tank will be filled with water to 0.55 m height. Calculate:

a) the volume of water in litres. b) the area of glass that needs replacing for the four sides and base (m²). State which faces you include and justify.

4. A rural water tank has a vertical cylindrical body of radius 1.5 m and height 4.0 m with a hemispherical dome on top (same radius). Calculate:

a) the total volume of water the tank can hold (m³). b) the external surface area that needs painting (include the curved surface of the cylinder and hemisphere but not the base that sits on the ground). Show formulas and reasoning.

5. A living room floor is rectangular 5.0 m by 4.0 m but has a rectangular alcove removed measuring 1.5 m by 1.0 m. Calculate:

a) the floor area (m²). b) the perimeter of the resulting floor shape around the outside (m) — explain how you account for the alcove when finding the perimeter.

✏️ Part 2: Short Justifications and Conversions

6. A storage box measures 80 cm × 50 cm × 60 cm. Convert its volume to cubic metres and litres. Show your unit conversion steps and final answers.

7. State the formula for the surface area of a rectangular prism and briefly justify why that formula counts every face once. (Use words or a short sketch description.)

8. Explain in 2–3 sentences the difference between perimeter, area and surface area. Give one real-world example when surface area is the key measure to use instead of volume or perimeter.