Solid properties, plans and elevations · Higher
| English | 中文 | Pinyin |
|---|---|---|
| elevation/ˌelɪˈveɪʃn/ | 立面图 | lì miàn tú |
A building plan shows the footprint but hides its height. Front and side elevations add information that a single view cannot show.
- A building plan shows the footprint but hides its height. Front and side elevations add information that a single view cannot show.
- This lesson studies elevation 立面图: An orthographic view from a stated horizontal direction.
Choose the mathematical structure
- A face is a flat boundary polygon; curved surfaces must be named separately. Edges join faces and vertices are corners. A prism has two congruent parallel end faces and a constant cross-section. A pyramid joins one polygon base to an apex. Plan is the view from above; front and side elevations are direct views without perspective. Give the viewing direction and align corresponding widths, depths and heights.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines elevation?
An orthographic view from a stated horizontal direction.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A cube or cuboid has 6 faces, 12 edges and 8 vertices. A triangular prism has 5 faces, 9 edges and 6 vertices; a square pyramid has 5 faces, 8 edges and 5 vertices. A cylinder has two circular flat faces and one curved surface, with no vertices. A cone has one flat circular face, one curved surface and one apex; a sphere has only a curved surface. For a cuboid of width 4, depth 3 and height 2 units, the plan is 4 by 3, front elevation 4 by 2 and side elevation 3 by 2. A stack with front-row column heights 1 and 3, and back-row heights 2 and 1, occupies four cells. The front elevation has column maxima 2 and 3; the side elevation has depth-row maxima 3 and 2. These views do not determine every hidden cube uniquely.
Solid properties, plans and elevations
A face is a flat boundary polygon; curved surfaces must be named separately
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
How many edges does a triangular prism have?
Three edges on each triangular end plus three joining edges: 3+3+3.
Test a tempting shortcut
- Do not draw perspective diagonals in an orthographic elevation. A plan alone cannot give height. Different hidden arrangements can share the same plan and elevations; do not claim a unique reconstruction without enough information.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A plan view always determines the height of a solid. This claim is false. Explain which definition or assumption it violates.
Find the plan area of a cuboid width 4, depth 3, height 2.
Plan uses width and depth: 4×3=12 square units.
A plan view always determines the height of a solid.
Do not draw perspective diagonals in an orthographic elevation. A plan alone cannot give height. Different hidden arrangements can share the same plan and elevations; do not claim a unique reconstruction without enough information.
Interpret a new situation
- AQA G12/G13 covers the named solids and construction/interpretation of views. Label dimensions and directions, preserve alignment between views and explain any hidden-space ambiguity.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the front-elevation area for that cuboid.
Front uses width and height: 4×2=8 square units.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
An orthographic view from a stated horizontal direction. Choose the relationship, show the method, check its assumptions and interpret the result.