📐 Week 2: Rua Kūmara Volume Calculation
Unit 10: Kai, Culture and Climate — Surviving Scarcity
Calculate how many kūmara could be stored in a rua kūmara (storage pit). This connects mathematics to understanding how Māori managed food scarcity.
📏 Step 1: Measure Your Model Rua
If you built a model rua kūmara, measure it. If not, use these example measurements:
| Measurement | Your Model | Example (Real Size) |
| Length (cm) | _____ cm | 200 cm (2 m) |
| Width (cm) | _____ cm | 150 cm (1.5 m) |
| Depth/Height (cm) | _____ cm | 100 cm (1 m) |
🧮 Step 2: Calculate Volume
Volume = Length × Width × Height
(For a rua kūmara, we'll treat it as a rectangular box)
Your Calculations:
Volume = _____ cm × _____ cm × _____ cm
Volume = _____ cm³
Convert to cubic meters (m³):
1 m³ = 1,000,000 cm³
Volume = _____ cm³ ÷ 1,000,000 = _____ m³
🍠 Step 3: Estimate Kūmara Storage
Assumptions:
- An average kūmara is about 15 cm long and 8 cm wide (roughly the size of a large potato)
- Kūmara are stored with some space between them (not packed tightly)
- About 60% of the rua space is actually filled with kūmara (40% is air space)
Calculate:
1. Volume of one kūmara (approximate):
Volume of kūmara ≈ _____ cm³
2. How many kūmara could fit (if packed tightly):
Number = Rua volume ÷ Kūmara volume
Number = _____ ÷ _____ = _____ kūmara
3. Account for air space (use 60%):
Actual storage = _____ × 0.6 = _____ kūmara
🤔 Step 4: Reflection Questions
- How many people could this rua feed? (Assume 1 person eats 2-3 kūmara per day, and storage needs to last 3-4 months)
- What if the rua was bigger/smaller? How would that change the number of kūmara stored?
- Why was storing kūmara important? What would happen if you couldn't store them?