3-D shapes (age 9+)
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
What a learner can do afterwards
- Identify a cuboid from its net
- Name the 3-D shape shown in an isometric drawing
- Match 2-D representations to the correct 3-D shape
1 · Read
You already know how a net folds up into a solid shape. Now flip that idea around: look at a flat picture and name the 3-D shape it stands for.
A cuboid net is six rectangles joined the right way, like the faces of a box. Each flat piece becomes one face. If all six are same-size squares, that box is a special cuboid called a cube.
Priya looks at a net with one square and four triangles attached to its sides. The triangles meet at a point when folded, so Priya knows this net makes a pyramid, not a cuboid.
An isometric drawing uses slanted lines so a flat picture looks solid, like you are looking at the corner of a real box. Count the flat faces and check the corners to name the shape. A box with six rectangle faces is a cuboid.
A cube has every edge the same length, like a dice. A cuboid can have edges of different lengths, like a shoebox. A pyramid has triangle faces meeting at one point above a flat base. In an isometric drawing, a cube shows equal edges, but a cuboid that is not a cube shows uneven edges.
A flat picture, like a net or an isometric drawing, is a clue that names the 3-D shape hiding inside it.
More to read
5.1: Polyhedra
Polyhedra are 3-D shapes with flat faces. Cubes, cuboids, pyramids, and prisms all belong to the family. Each face is a polygon, edges are where faces meet, and vertices are the corner points. Learn shapes by counting parts. A cuboid has 6 rectangular faces, 12 edges, and 8 vertices. A square-based pyramid has 1 square plus 4 triangles.
5.2: Nets and Surface Area
A net is a solid unfolded flat. A cuboid opens into 6 rectangles joined edge to edge. A cube opens into 6 squares, often in a cross shape with one square on the side. Match nets to solids by picturing the fold. If opposite faces match in size, a box can close. A net of 1 square and 4 triangles folds into a square-based pyramid.
5.3: More Nets, More Surface Area
Trickier solids need trickier nets. A cylinder unwraps into 2 circles plus 1 rectangle that rolls around them. A triangular prism shows 2 triangles plus 3 rectangles. Isometric drawings show 3-D shapes on flat paper with slanted depth lines. A cube looks like a square with a shifted square behind it, joined at the corners. Read the depth lines to name the solid.
6.2: Surface Area of a Cube
Cubes are the tidiest solids of all. All 6 faces are identical squares, all 12 edges match, and all 8 vertices look alike. A dice is a cube you already know. A cube is a special cuboid with all edges equal. Every cuboid rule covers cubes too. If a box has square faces everywhere, call it a cube.
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2 · Watch
به انگلیسیTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.