🌲 Part 1: Forestry Area Calculations

1. A rectangular forestry block needs to be planted with native trees. If the block is 150 metres long and 80 metres wide, what is the total area that needs planting?

2. Which unit would be most appropriate for measuring the area of a large forestry plantation?

Square centimetres (cm²)

Square metres (m²)

Square kilometres (km²)

Hectares (ha)

3. A forester needs to calculate the area of an irregularly shaped forest block. The block can be divided into two rectangles: one measuring 200m × 120m and another measuring 180m × 90m. What is the total area?

📏 Part 2: Log Volume Calculations

4. A cylindrical log has a diameter of 60 centimetres and a length of 4 metres. Calculate the volume of timber in this log. (Use the formula: Volume = π × r² × h, where π ≈ 3.14)

5. Convert your answer from question 4 into cubic metres (remember: 1 cubic metre = 1,000,000 cubic centimetres).

6. A logging truck carries 5 logs with the following dimensions. Calculate the total volume of timber:

• Log 1: diameter 50cm, length 3.5m

• Log 2: diameter 45cm, length 4m

• Log 3: diameter 55cm, length 3m

• Log 4: diameter 40cm, length 4.5m

• Log 5: diameter 60cm, length 3.5m

🏗️ Part 3: Forestry Career Connections

7. Match each forestry career with the main mathematical skill they would use most often:

1. Forest Manager

2. Logging Equipment Operator

3. Timber Grader

4. Environmental Scientist

A. Volume calculations for timber quality

B. Area calculations for plantation planning

C. Statistical analysis of forest health data

D. Measurement and spatial reasoning for machinery operation

8. Which mathematical skills are important in forestry? (Check all that apply)

Calculating areas and volumes

Using measurement tools accurately

Converting between different units

Analysing data and statistics

Problem-solving with real-world constraints

Using scale factors and proportions

🌿 Part 4: Real-World Applications

9. A forestry company plants trees in rows that are 3 metres apart. If they plant 25 rows in a rectangular block that is 200 metres long, what is the width of the planted area?

10. Fill in the blanks about forestry measurements:

In New Zealand forestry, land area is commonly measured in __________ (unit), while timber volume is measured in __________ (unit). When measuring the diameter of a tree trunk, foresters typically use __________ as the unit of measurement.

11. A sustainable forestry plan requires replanting 150% of the area that was harvested. If 45 hectares were harvested this year, how many hectares need to be replanted?

12. Draw a diagram showing how you would measure the diameter and length of a log to calculate its volume. Label your diagram clearly.