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GCSE/Mathematics/OCR

G13Interpret and construct plans and elevations of 3D shapes

Notes

Plans and elevations

OCR J560 expects fluent translation between a 3D solid and its three orthographic views. Plans and elevations appear on every Foundation paper and frequently on Higher.

The three standard views

  • Plan view — the view looking straight down on the object from above.
  • Front elevation — the view looking horizontally at the front face.
  • Side elevation — the view looking horizontally from the side (usually the left).

Each view is a 2D drawing showing the outline as it would appear with parallel projection (no perspective). All measurements are true to scale.

Conventions

  • Use a sharp pencil and ruler. Lines that are visible in the view are solid; hidden edges (behind another face) are usually shown dashed when asked.
  • Each view should be drawn on a separate part of the grid. OCR mark schemes typically award B1 per correct view, with shape and dimensions both required.
  • Always label which view is which — "Plan", "Front", "Side".

Building from views

Going the other way — given the three views, sketch the solid — is harder. Read each view as constraints:

  • Plan tells you the footprint (base shape).
  • Front elevation tells you the height and front-facing profile.
  • Side elevation confirms depth and any features hidden from the front.

A common OCR question: an L-shaped block. Plan is an L. Front shows the tall and short heights. Side shows the depth. Total volume = sum of two cuboids.

Worked example

A staircase solid (two-step) sitting on a 6×4 cm base, total height 4 cm in two equal 2 cm steps:

  • Plan: rectangle 6 × 4 cm with an internal line at 3 cm splitting it.
  • Front elevation: an L-shape — full 6 cm wide, 4 cm tall on the back half, dropping to 2 cm on the front half.
  • Side elevation: rectangle 4 × 4 cm.

OCR mark scheme conventions

  • B1 per view drawn correctly with correct shape and dimensions.
  • Loss of mark for missing dimensions or wrong proportions on grid paper.
  • Hidden lines only required if the question states "show hidden edges".

Common mistakes

  1. Drawing a perspective sketch instead of an orthographic view.
  2. Confusing front and side elevation directions.
  3. Ignoring the squared grid scale (e.g. each square = 1 cm).

AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 16 marks

    Three views of a cuboid step

    OCR J560/02 — Foundation (calculator)

    A solid is made from two cuboids stacked: bottom cuboid 6 cm × 4 cm × 2 cm, top cuboid 3 cm × 4 cm × 2 cm placed flush at the back-left corner.

    (a) Draw the plan view. [2]
    (b) Draw the front elevation (looking from the long side). [2]
    (c) Draw the side elevation. [2]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves

  2. Question 23 marks

    Identifying the solid

    OCR J560/01 — Foundation (non-calculator)

    A solid has the following views on a 1 cm grid:

    • Plan: a circle of radius 3 cm.
    • Front elevation: a rectangle 6 cm wide and 5 cm tall.
    • Side elevation: a rectangle 6 cm wide and 5 cm tall.

    (a) Name the solid. [1]
    (b) State its dimensions. [2]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves

  3. Question 33 marks

    Volume from views

    OCR J560/05 — Higher (calculator)

    The plan view of a solid is an L-shape made from a 5 × 3 rectangle with a 2 × 1 rectangle removed from the top-right corner. The front elevation is a rectangle 5 cm × 4 cm. All faces are vertical or horizontal.

    Calculate the volume of the solid. [3]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves

Flashcards

G13 — Interpret and construct plans and elevations of 3D shapes

7-card SR deck for OCR GCSE Mathematics J560 (leaf top-up — batch 4) topic G13

7 cards · spaced repetition (SM-2)