Scenario: A construction company is building a warehouse with a rectangular base and a triangular prism roof. The rectangular warehouse base measures 20 metres by 15 metres with a height of 8 metres. The triangular roof has a base of 15 metres and the sloped sides meet at a peak 6 metres above the rectangular section. The company needs to calculate costs for painting the exterior walls and roof (excluding the ground), and determine the total storage volume. Paint costs $12 per square metre, and storage rental rates are $8.50 per cubic metre per month.

1. Use Pythagoras' theorem to find the length of the sloped roof edge.

2. Calculate the angle of elevation of the roof using trigonometry.

3. Find the total surface area that needs painting (all exterior walls and roof surfaces, excluding the ground).

4. Calculate the total volume of the warehouse (rectangular section + triangular roof section).

5. Determine the total cost of painting the exterior surfaces.

6. If the warehouse is rented at $8.50 per cubic metre per month, what would be the monthly rental income?

7. Express the ratio of the rectangular prism volume to the triangular prism volume in its simplest form.

8. Calculate the rate of painting cost per cubic metre of storage space (painting cost ÷ total volume).

9. Explain how changing the roof angle would affect both the surface area and volume calculations.