- Write down the number of faces, edges and vertices of a cuboid.[2]
Loading...
Architects cannot hand builders a 3D model, so they draw flat views instead: the view from above (the ), from the front (the ) and from the side (the ). This lesson covers the faces, edges and vertices of 3D solids and how to move between a solid and its views.
The big picture
Each view flattens the solid by looking straight at it from one direction. Depth disappears, so a view shows only the outline and any edges you would see as lines.
Going backwards — building a solid from its three views — is the harder skill. Each view limits what is possible, and combining all three narrows it down to a single shape, or a small set of possibilities.
What you'll learn
A is a flat surface, an is where two faces meet, and a is a corner.
Cuboid: 6 faces, 12 edges, 8 vertices. Triangular prism: 5 faces, 9 edges, 6 vertices. Square-based pyramid: 5 faces, 8 edges, 5 vertices.
For these solids, faces vertices edges — a useful check on your counts.
How many edges does a hexagonal prism have?
Plan: look straight down. Front elevation: look from the front. Side elevation: look from the side.
A cylinder standing upright has a circle as its plan and rectangles as both elevations.
A square-based pyramid has a square with its diagonals as its plan, and triangles as its elevations.
Tip — Draw on squared or isometric paper and use the dimensions given — elevations must be to scale.
Match the widths: the plan and front elevation share the same width; the plan and side elevation share the same depth.
For solids made of cubes, the front elevation gives the tallest column in each position across, and the side elevation the tallest in each position front-to-back.
A solid has a circular plan, and its front and side elevations are both triangles. Name the solid.
Two different solids can share the same three views. When a question asks for the "greatest" or "least" number of cubes, it is using that fact.
Think like an examiner
Remember these
Watch out for these
Stretch yourself
A solid is made from identical cubes. Its plan is a grid of 3 squares across and 2 deep, all filled. The front elevation (3 across) shows column heights 2, 1, 1. The side elevation (2 deep) shows heights 2, 2. Find the number of cubes used.
Hint — Every square in the plan has at least one cube. Only the left column can be 2 tall.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
The front elevation and side elevation of a solid are both rectangles measuring 4 cm by 6 cm. The plan is a square of side 4 cm.
Test yourself
Ready to practise Plans & Elevations? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Plans & Elevations, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.