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
The lesson
You already know that 3-D shapes have faces, edges, and vertices. Now you will count these for shapes with more parts, 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 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.
Watch it
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.
8 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.