G13: Plans & Elevations
Construct and interpret plans and elevations of 3D shapes
📋 Key Concepts
Plans and elevations are 2D views of a 3D shape, showing what it looks like from different directions.
Three main views:
- Plan view: Looking down from above (bird's eye view)
- Front elevation: Looking from the front
- Side elevation: Looking from the side
📝 Plan View
Plan view: Shows the shape as seen from directly above. This is the "footprint" of the shape.
Example 1
Draw the plan view of a cuboid 4 cm × 3 cm × 2 cm (length × width × height).
Solution:
Looking from above, you see the length and width.
Plan view is a rectangle 4 cm × 3 cm.
The height (2 cm) is not visible from above.
📝 Front Elevation
Front elevation: Shows the shape as seen from the front. Shows the height and width of the front face.
Example 2
Draw the front elevation of a cuboid 4 cm × 3 cm × 2 cm, viewed from the 4 cm × 2 cm face.
Solution:
Front elevation is a rectangle 4 cm × 2 cm.
This shows the height and length of the front face.
📝 Side Elevation
Side elevation: Shows the shape as seen from the side. Shows the height and depth.
Example 3
Draw the side elevation of a cuboid 4 cm × 3 cm × 2 cm, viewed from the side (3 cm × 2 cm face).
Solution:
Side elevation is a rectangle 3 cm × 2 cm.
📝 Combining Views
Important: All three views together give complete information about a 3D shape.
Example 4
A shape has: Plan view = square, Front elevation = rectangle, Side elevation = rectangle. What could the shape be?
Solution:
Plan view = square → top face is square
Front and side = rectangles → could be a square-based prism or cube
If all views are squares → cube
📝 Drawing Elevations from Isometric Views
Example 5
An L-shaped block is made from two cuboids. Draw the plan, front and side elevations.
Solution:
Plan view: Look down - shows L-shape from above
Front elevation: Look from front - shows height and width, accounting for different heights
Side elevation: Look from side - shows height and depth
Tip: Use squared paper and count squares carefully.
📝 Interpreting Views
To interpret views:
- Look at each view carefully
- Identify the dimensions shown in each view
- Combine information to build a mental 3D image
- Check if hidden edges are shown with dotted lines
Example 6
Plan = circle, Front elevation = rectangle, Side elevation = rectangle. What is the shape?
Solution:
Plan = circle → circular base
Front = rectangle → vertical sides
Side = rectangle → confirms vertical sides
This is a cylinder.
❓ Practice Questions
Q1: What does the plan view show?
Q2: A cuboid has dimensions 5 cm × 4 cm × 3 cm. Draw the front elevation (viewing the 5 cm × 3 cm face).
Q3: What 3D shape has a circular plan view and a rectangular front elevation?
Q4: A triangular prism has a triangular cross-section. What shape is the front elevation?
Q5: If plan view = triangle, what could the 3D shape be?
✅ Answers
- The view from above (bird's eye view)
- A rectangle 5 cm × 3 cm
- Cylinder
- A rectangle (the side faces of the prism)
- Triangular prism, tetrahedron, or triangular-based pyramid
🎯 Exam Tips
- Always label which view you are drawing
- Use a ruler and draw on squared paper
- Hidden edges are shown with dotted lines
- Check dimensions carefully - count squares
- Plan view shows length × width
- Elevations show height combined with another dimension
🧠 Problem-Solving Strategies
Problem-Solving
Plan view = looking from above (top). Front elevation = looking from the front. Side elevation = looking from the side. Hidden edges are shown with dashed lines. Use squared paper for accuracy. Start by identifying the overall dimensions, then add detail. Match features across different views to build a 3D picture.
Multi-Step Problem
A shape made from cubes has the front elevation: 3 squares tall on the left, 1 square tall on the right. The side elevation: 2 squares tall on the left, 1 square tall on the right. What is the minimum number of cubes needed?
Solution: Front shows 4 visible squares (3+1). Side shows 3 visible squares (2+1). The minimum arrangement uses 5 cubes: 3 stacked at the back-left (seen as 3 in front, 2 in side), 1 at back-right (seen as 1 in front, 1 in side), and 1 at front-left row 2 height (seen as part of the 3-high column from front, part of 2-high from side). Minimum = 5 cubes.
⚠️ Common Errors
Watch Out!
1. Wrong: Drawing the front elevation from a different direction than specified Correct: Always check which direction is the "front". The front elevation is what you see looking from the front face of the object as given in the question.
2. Wrong: Forgetting to show hidden edges with dashed lines Correct: Edges that are behind other faces (not visible from the viewing direction) must be drawn as dashed lines, not omitted.
3. Wrong: Confusing the plan view with the front elevation Correct: Plan view is from ABOVE (bird's eye view). Front elevation is from the FRONT (eye level). They show completely different information about the same object.
✍️ 6-Mark Exam Question
Extended Answer
6 marks: A solid is made from a cuboid 8 cm x 4 cm x 6 cm with a hemispherical depression of radius 2 cm cut from the top face. (a) Draw the plan view of the solid. (b) Draw the front elevation. (c) Calculate the volume of the solid, giving your answer to 3 significant figures.
(a) Plan view: a rectangle 8 cm x 4 cm with a circle of radius 2 cm visible inside (the hemisphere seen from above appears as a full circle).
(b) Front elevation: a rectangle 8 cm x 6 cm with a semicircular cut-out of radius 2 cm at the top centre.
(c) Cuboid volume = 8 x 4 x 6 = 192 cm cubed. Hemisphere volume = 1/2 x 4/3 x pi x 2 cubed = 2/3 x pi x 8 = 16.76 cm cubed. Solid volume = 192 - 16.76 = 175.24 = 175 cm cubed (3 s.f.).
Mark scheme: M1 plan with circle, A1 correct plan, M1 front with semicircle, A1 correct elevation, M1 volume calculations, A1 175 cm cubed
📊 AO3: Reason & Interpret
Reasoning and Interpretation
A student sees the plan view of a shape: a 4x3 rectangle. The front elevation: a 4x2 rectangle. The side elevation: a 3x2 rectangle.
(a) Could this be a cuboid? If so, what are its dimensions?
(b) The student says "The plan view tells me the height is 2." Is this correct?
(c) Another shape has a circular plan view but a triangular front elevation. Describe a possible 3D shape.
Answers: (a) Yes — a cuboid with dimensions 4 x 3 x 2. Plan = 4x3 (length x width from above), front = 4x2 (length x height), side = 3x2 (width x height). (b) No — the plan view shows only length and width (from above). The height is NOT visible in plan view. The height of 2 comes from the front or side elevation. (c) A cone viewed from above shows a circle (plan). Viewed from the side, it shows a triangle (front elevation). This could be a cone.
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🎬 Video Resources
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