Part A — Volume, Capacity & Cost
Designing real objects links volume (space inside, in m³), capacity (how much it holds, in litres) and cost. A useful conversion: 1 m³ = 1000 L.
1
A garden bed is 3 m long, 2 m wide and 0.3 m deep. Find its volume in cubic metres.
Volume = m³
2
Convert that volume to litres. (Remember 1 m³ = 1000 L.)
Answer: L
3
Soil is sold in 30 L bags. How many bags are needed to fill the bed?
Answer: bags
4
Each bag of soil costs $8. What is the total cost to fill the bed?
Answer:
5
A second bed is the same width and depth but twice as long. Without redoing all the working, explain how the volume and the number of bags change.
6
Design challenge. Design a rectangular garden bed with a volume as close as possible to 1 m³. Give its length, width and depth, and show the volume.
Part B — Measuring & Costing Real Spaces
Modelling a real job means choosing the right measure: perimeter for things that go around an edge (fencing, edging), and area for things that cover a surface (paving, paint). Watch your units and convert when needed.
1
A rectangular yard is 8 m by 5 m. Find the perimeter, then the cost of fencing it at $15 per metre.
2
The same yard is to be paved. Find its area, then the cost at $40 per square metre.
3
Complete these conversions.
(a) 2.5 m = cm
(b) 3500 mL = L
(c) 1.2 kg = g
4
Estimate, then calculate. A tin of paint covers 10 m². A wall is 4 m wide and 2.5 m high. Estimate, then work out how many tins are needed.
5
Reasoning. A square garden of side 6 m has a 1 m-wide path running all the way around the outside. What is the area of the path only?
6
Design and cost. Plan a rectangular vegetable plot no larger than 12 m². State its dimensions, the length of edging it needs, and the cost of edging at $6 per metre.