3-D shapes (age 11+)
Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections
What a learner can do afterwards
- Count and describe the faces, edges, and vertices of a triangular prism and a square-based pyramid
- Describe the 2-D cross-section produced by slicing a cylinder horizontally or a cone vertically
- Use properties of 3-D shapes to determine whether a given net will fold into a specified solid
1 · Read
You have already matched the flat pieces in a net to a solid, like six squares making a cube. Now you will count those parts for solids like a triangular prism or a square-based pyramid. A face is a flat surface, an edge is where two faces meet, and a vertex is a point where edges meet. A triangular prism has 5 faces, 9 edges, and 6 vertices. A cone cut straight down through its tip makes a triangle.
A square-based pyramid has one square face on the bottom and four triangle faces that meet at a point on top. That makes 5 faces. It has 8 edges: 4 around the square base and 4 running up to the top point. It has 5 vertices: the 4 corners of the square, plus the point at the top.
To check if a net folds into a solid, match every flat shape in the net to a face on that solid. A cube's net needs exactly 6 squares. A triangular prism's net needs 2 triangles and 3 rectangles, so a net with only 1 triangle is missing a face.
The angle of a cut changes the cross-section. Slice a cylinder straight across and you get a circle. Slice it at an angle instead, and the circle stretches into an oval.
Faces, edges, and vertices describe a solid, and the way you slice or unfold it can reveal a completely different 2-D shape.
Includes readings credited to the academy collection. Rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
Learn first
This opens up
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.