VCE VCE VM Numeracy (Year 12) · Unit 3 — Number, Shape, Measures and Relationships · 12m read

Quantity and Measures — Units, Conversions, Perimeter, Area and Volume

Measurement is the most used workplace maths — ordering materials, cooking, building and planning all depend on it.

Learning objective: Measure and calculate length, area, volume, capacity, mass and time, converting units accurately for practical tasks.

By the end of this lesson you can:

• I can convert between metric units.
• I can calculate perimeter, area and volume for practical jobs.
• I can calculate quantities and costs of materials, including waste allowance.

Measure twice, cut once. A careful calculation saves money, materials and time.

Units and formulas

CONVERSIONS
• Length: 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km.
• Mass: 1000 g = 1 kg; 1000 kg = 1 tonne.
• Capacity: 1000 mL = 1 L; 1 cm³ = 1 mL; 1 m³ = 1000 L.
• Area: 1 m² = 10 000 cm².

FORMULAS
• Perimeter: add all sides; circle circumference = π × diameter (π ≈ 3.14 or 22/7 — both are acceptable approximations).
• Area: rectangle = length × width; triangle = ½ × base × height; circle = π × r².
• Volume: rectangular prism = l × w × h; cylinder = π × r² × h.

MATERIALS: add a WASTE allowance (often around 10%) when ordering tiles, paint or timber.

Worked example (Medium)

A room is 4.2 m × 3.5 m. Tiles cost $38 per m² and you need 10% extra for waste. Find the cost.

1. Area. 4.2 × 3.5 = 14.7 m².
2. Add waste. 14.7 × 1.1 = 16.17 m².
3. Cost. 16.17 × 38 ≈ $614.46.

Answer: About $614.46 (order 16.2 m², or round up to whole boxes as sold).

Worked example (Medium)

A cylindrical water tank has radius 1 m and height 2 m. How many litres does it hold?

1. Volume. π × 1² × 2 ≈ 3.14 × 2 = 6.28 m³ (with 22/7: ≈ 6.29 m³).
2. Convert. 1 m³ = 1000 L.

Answer: About 6280 L (≈ 6290 L using 22/7 — either approximation is fine).

Common mistakes

• Mixing units (m and cm) in one calculation Answers are wrong by factors of 100 or more. Fix: Convert to one unit before calculating.
• Ordering the exact area Cuts and breakages need extra. Fix: Add a waste allowance and round up to whole packs.

Practice questions

1. 2.5 m³ of water is how many litres?

   1. 25 L
   2. 250 L
   3. 2500 L
   4. 25 000 L

   (1 marks)

2. A fence runs around a 12 m × 8 m yard with a 1 m gate. Fencing costs $45 per metre. Find the cost.

   (3 marks)

Summary

• Convert to consistent units first.
• Use area and volume formulas for practical jobs.
• Add waste allowances and round up when ordering.
• π ≈ 3.14 or 22/7 — both acceptable.