--- title: "3-D shapes (age 11+)" description: "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" canonical: https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR source: https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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 Subject: Mathematics · Area: Geometry · Ages 11 to 13 Page: https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR ## Ready when they can - 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 ## Lesson: Counting faces and picturing cross-sections 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. *(drawing: Slice a cylinder straight across, like cutting a tin of beans in half. The flat surface you reveal is a circle, the same shape as the cylinder's base.)* **Example.** 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. **Recap.** Faces, edges, and vertices describe a solid, and the way you slice or unfold it can reveal a completely different 2-D shape. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [3-D shapes (age 10+)](https://lightmysky.com/learn/mathematics/3-d-shapes-age-10-mt_REwgr0d_ss) - [3-D shapes (age 9+)](https://lightmysky.com/learn/mathematics/3-d-shapes-age-9-mt_wUSbRt3-qw) ## Opens up - [Surface Area of Solids](https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc)