Part B — 5 × 5-mark questions
6. Unit-cube prism. A rectangular prism is 7 cubes long, 5 cubes wide and 4 cubes high. (a) Find the number of cubes. (b) Write V=lwh. (c) Recalculate using base area × height. (d) Explain why the methods agree. (e) State the volume units.
7. Triangular prism. A triangular prism has triangle base 18 cm, triangle height 12 cm and prism length 15 cm. (a) Find cross-sectional area. (b) Find volume. (c) Explain “constant parallel cross-section”. (d) Predict what happens if the length doubles. (e) Connect this to V=Bh.
8. Building model. A high-rise has floor area 250 m², 12 identical storeys and each storey is 3 m high. (a) Find total height. (b) Estimate enclosed volume. (c) Explain why floor area × number of storeys is not itself a volume. (d) State one modelling assumption. (e) Explain how changing storey height affects the result.
9. Invariance. A dynamic model changes a prism's shape while keeping cross-sectional area 40 cm² and perpendicular length 12 cm. (a) Find volume. (b) Explain why slanted edge lengths can change without changing volume. (c) State the two quantities that control V. (d) Describe a change that would double V. (e) Describe a different change that keeps V constant.
10. Reverse problem. A prism has volume 756 cm³ and cross-sectional area 42 cm². (a) Find length. (b) If area doubles, find the new length required to keep volume unchanged. (c) Explain the inverse relationship. (d) Check both products. (e) State why consistent units matter.
Part C — Enrichment investigation
A ranger team is estimating the capacity of a long rock-shelter void using a triangular-prism approximation. Use a hypothetical triangular cross-section with base 30 m and perpendicular height 12 m, and prism lengths 20 m, 25 m, 30 m and 35 m.
1. Find the cross-sectional area. 2. Make a table of volumes. 3. Describe the relationship between length and volume. 4. Explain what assumptions make the prism model reasonable or unreasonable. 5. Discuss how geometric models can support environmental monitoring while recognising that real landforms are irregular and cultural knowledge should not be reduced to a single geometric model.