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Sustainable City Design Math

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Sustainable City Design Math

A coastal council is redesigning a small, low-emissions neighbourhood. Use measurement, area, volume, scale and unit conversions to test the plans. Show working and include units in every answer. Use π = 3.14 where needed.

Fit the park into the block

The council has a rectangular block measuring 180 m by 120 m. It will reserve 35% of the land for a park and native planting.

1.Find the total area of the block in square metres and hectares. (1 ha = 10,000 m²)

2.How many square metres should be set aside for the park and native planting?

3.A proposed rectangular park is 90 m long and 80 m wide. Does it meet the 35% land allocation? Calculate its area and state how many square metres it is above or below the target.

Make the drawing to scale

The planning team uses a scale of 1 cm : 20 m. The block is 180 m by 120 m.

4.What dimensions, in centimetres, should the block have on the scale plan?

5.On the same scale plan, a bike path is 2.5 cm long. What is its actual length in metres?

Draw a 9 cm by 6 cm rectangle to represent the block. Inside it, sketch and label a park, apartments, shops and a bike path. Keep your drawing to scale where possible.

Measure the buildings and water

Use the proposed dimensions below to check whether the designs are practical.

6.An apartment building has a rectangular footprint 32 m by 24 m and is 21 m tall. Find its footprint area and its volume.

7.A rainwater tank is a rectangular prism measuring 2.4 m long, 1.5 m wide and 1.2 m high. Find its capacity in cubic metres and litres. (1 m³ = 1,000 L)

8.The tank is currently 75% full. How many litres of water are in it, and how many more litres can it hold?

Check the outdoor finishes

The council wants permeable paving around the park. Its rectangular paved plaza will measure 18 m by 12 m.

9.A paving supplier sells packs that cover 6 m². What is the minimum number of packs needed to cover the plaza?

10.A circular garden pond has a radius of 4 m. Find its area to the nearest hundredth of a square metre. Use A = πr² and π = 3.14.

11.A contractor says the plaza needs 30 packs of paving. Is that enough? Justify your answer using the area and pack coverage.

TrueFalse

12.The design team wants to increase the park allocation from 35% to 40%. How many additional square metres would that require on the 21,600 m² block?