3D Shapes, Plans and Elevations
A 3D, or three-dimensional, shape, or solid, has faces, flat or curved surfaces, edges, where two faces meet, and vertices, corner points, and a net is a 2D shape that folds up to make one. The plan of a solid is the view looking straight down from above, the front elevation is the view looking straight at the front, and the side elevation is the view looking straight at the side, each of which is a rectangle for a cuboid.
Before you start
Make sure you're comfortable with these topics first:
Method
- To describe a solid, count its faces (flat surfaces), edges (the line where two faces meet) and vertices (corners where edges meet).
- To find or check the number of faces, edges and vertices, use Euler's formula: faces + vertices - edges = 2, for any solid with flat faces.
- To sketch or identify a net, imagine unfolding every face of the solid flat, keeping edges that were joined on the solid joined on the net.
- For the plan, front elevation and side elevation of a cuboid, use two of its three dimensions for each view: plan = length by width, front elevation = length by height, side elevation = width by height.
- For a solid made of unit cubes, build up each view square by square, using the tallest stack of cubes in each direction to decide the height shown in that view.
- Label each view clearly (plan, front elevation, side elevation) and give the dimensions of each, since the three views together fully describe the solid.
Worked example
A cuboid is 6 cm long, 4 cm wide and 3 cm tall. State the dimensions of (a) its plan, (b) its front elevation, (c) its side elevation.
- The plan is the view from directly above, so it shows the length and the width: 6 cm by 4 cm.
- The front elevation is the view from directly in front, so it shows the length and the height: 6 cm by 3 cm.
- The side elevation is the view from directly at the side, so it shows the width and the height: 4 cm by 3 cm.
Practice questions
Try each question, then tap to reveal the answer.
Q1State the number of faces, edges and vertices of a cube.Show answer
Answer: 6 faces, 12 edges, 8 vertices
Q2State the number of faces, edges and vertices of a triangular prism.Show answer
Answer: 5 faces, 9 edges, 6 vertices
Q3State the number of faces, edges and vertices of a square-based pyramid.Show answer
Answer: 5 faces, 8 edges, 5 vertices
Q4A solid has 8 faces and 12 vertices. Use Euler's formula (faces + vertices - edges = 2) to find its number of edges.Show answer
Answer: 8 + 12 - edges = 2, so edges = 8 + 12 - 2 = 18
Q5A tetrahedron (triangular-based pyramid) has 4 faces and 4 vertices. Use Euler's formula to find its number of edges.Show answer
Answer: 4 + 4 - edges = 2, so edges = 6
Q6A cuboid is 10 cm long, 5 cm wide and 7 cm tall. State the dimensions of its front elevation.Show answer
Answer: 10 cm by 7 cm (length by height)
Q7A cuboid is 12 cm long, 8 cm wide and 5 cm tall. State the dimensions of its plan.Show answer
Answer: 12 cm by 8 cm (length by width)
Q8A solid is made from 2 identical unit cubes, one stacked directly on top of the other. State the shape and dimensions of (a) its plan, (b) its front elevation.Show answer
Answer: (a) the plan is a single unit square, 1 unit by 1 unit; (b) the front elevation is a rectangle 1 unit wide and 2 units tall
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A solid has 6 faces, 8 vertices and 12 edges. (a) Show that this solid satisfies Euler's formula. (b) Name a solid with these properties.
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A cuboid measures 9 cm by 6 cm by 4 cm (length by width by height). (a) State the dimensions of its plan, front elevation and side elevation. (b) A cube has the same volume as this cuboid. Show that the cuboid's volume is 216 cm^3, find the side length of the cube, and state whether this side length is greater than, equal to, or less than the cuboid's length of 9 cm.
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Free printable worksheet
Want more practice on paper? Download the 3d shapes, plans and elevations worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 20 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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