SkillrHub • Year 7 Maths

AC9M7SP01 • Homework

Representing 3D Objects in 2D

Use nets, aerial/plan views, isometric and perspective drawings, and orthographic views. Explain why a representation is suitable as well as what it shows.

5 × 2 marks
Short response
5 × 5 marks
Extended reasoning
1 enrichment
Representation design

Part A — Short response

  1. Define a net and give one object that can be constructed from a net. (2)
  2. State the faces needed in a triangular prism net. (2)
  3. What information does an aerial or plan view show particularly well, and what important dimension can it hide? (2)
  4. Give one advantage of an isometric drawing and one limitation of a perspective drawing. (2)
  5. Which two dimensions are normally visible in a front orthographic view? (2)

Part B — Extended response

  1. A packaging designer is making a triangular-prism box. Describe a valid net, explain how you would test it, and give one advantage and one disadvantage of using the net as the representation. (5)
  2. A simple house has a rectangular body and a pitched roof. Explain how an aerial view and a front view communicate different information, and name simple prisms that could approximate the structure. (5)
  3. Compare isometric, perspective and orthographic drawings. For each, state a useful purpose, then choose the best representation for a builder who needs exact dimensions and justify your choice. (5)
  4. A block object has the same front view as another object but a different top view. Explain how this is possible and why multiple orthographic views reduce ambiguity. (5)
  5. Explain how you would respectfully investigate a First Nations Australian artwork or cultural map of Country/Place as a two-dimensional representation. Include why you should not assume that symbols or mapping conventions have universal meanings. (5)

Part C — Enrichment

11. Representation challenge. Design a small structure made from at least two simple prisms. Produce or describe (a) a top/plan view, (b) a front view, and (c) an isometric or perspective view. Explain what each representation communicates well, what it hides, and which combination you would give to a builder. Justify your choices.

Answers / checking guide

1

A net is a 2D arrangement of faces that folds to make a 3D object; examples include a cube, rectangular prism, triangular prism or pyramid.

2

Two congruent triangles and three rectangles.

3

It shows footprint/layout well; height is usually hidden or unclear.

4

Example: isometric shows several faces and overall 3D form at once. Perspective can foreshorten lengths, so apparent lengths are not automatically true measurements.

5

Width and height.

6

A valid net has 2 triangles and 3 rectangles arranged to fold without overlap. Test by paper folding or a fold simulation. Advantage: all faces are visible for fabrication/surface planning. Limitation: assembled depth/orientation is harder to visualise.

7

The aerial view shows footprint/layout but little height; the front view shows width, height and roof profile but not full depth. A rectangular prism can approximate the body and a triangular prism the roof.

8

Isometric: useful 3D form, parallel axes; perspective: realistic depth but poor for direct measurement; orthographic: clear face-on dimensions but requires multiple views. Dimensioned orthographic views are strongest for construction.

9

A single front projection can hide depth or arrangement. The top view reveals horizontal placement/depth, while side views add further constraints; together the views reduce ambiguity.

10

Use reliable source/community context, describe the spatial or relational information actually supported, and avoid assigning universal meanings to symbols or assuming Western scale-map conventions.

11

Responses vary. Full-credit work should use internally consistent views, identify what each view preserves/omits, and justify a useful combination such as plan + elevations for dimensions with isometric/perspective for visualisation.