2-D faces on 3-D shapes
Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)
What a learner can do afterwards
- Identify and count circular flat faces on cones and cylinders, including faces left uncovered
- Identify triangular faces on a pyramid
- Recognise that the faces of 3-D shapes are 2-D shapes
- Identify pyramid bases and count or compare the faces of square-based and triangular pyramids
- Count cube and cuboid faces, including faces hidden from view
- Recognise that every cube face has the same size and shape
1 · Read
You have met flat shapes and solid shapes. Flat shapes are 2-D. Solids are 3-D. A face is a flat part on the outside of a solid. In this lesson, a curved surface is not a face. A sphere, like a ball, curves all over and has no flat faces.
A sphere has no flat faces.
A cylinder has two flat faces, one at each end. Both are circles. The surface around its side is curved. If you cover one circular end, the other circular end is still uncovered.
The circular ends look oval in this view of the cylinder.
A solid model cone has one flat circular face, called its base. Its pointed tip is not a face. Turning the cone does not change its base into a different shape. A cone has one circular face; a cylinder has two.
The cone's base is a circle, seen at a slant.
A rectangular paper label can wrap around a can's curved side. Take the label off and lay it flat. It has four straight sides and four square corners. Opposite sides match in length. The label is a rectangle. The wrapped side of the can is curved, not a flat face.
This shows the label after it is laid flat.
A pyramid's side faces are triangles. Each triangle has three straight sides. The side faces meet at a point, which is not a face. A square-based pyramid has a square base and four triangular sides: five faces. A triangular pyramid has a triangular base and three triangular sides: four faces.
This pyramid has a square base.
A cube has six square faces, all the same size and shape. A square has four equal straight sides and four square corners. To count the cube's faces, count top and bottom, front and back, then left and right. Those three pairs make six.
Every face of a cube is a square.
A cuboid is a box shape with six rectangular faces. Its top and bottom make one pair. Its front and back make another. Its left and right make the last pair. Each face is flat, although the whole box is solid.
Count all three pairs of faces.
A drawing can hide faces at the back or underneath a solid. Turn a model to find those faces too. Count each face once. Turning the model changes your view, but it does not change the shapes or number of its faces.
Some edges are dashed to show parts hidden from view.
Every face on a solid shape is a flat 2-D shape, like a circle, triangle, or square.
Lesson, practice questions and flashcards written for this dataset.
Readings and questions written for this dataset.
More to read
Which parts are faces?
Compare a model cone with a model cylinder. The cone has one flat circular base. The cylinder has a flat circle at each end. Both models also have curved surfaces. Here, we use face to mean a flat part. A curved surface does not count as a face. Check the surface itself: a round-looking outline does not tell you whether the surface is flat.
The base and the sides
A pyramid's base can have a different shape from its sides. A square-based pyramid has a square underneath and four triangles around it. A triangular pyramid has a triangle underneath and three triangles around it. Include the base when you count the faces. The point where the side faces meet is not another face.
Find the hidden faces
Hold a model cube and look at it from one place. Some faces may be hidden. Turn it to check underneath and behind. Count top and bottom, front and back, then left and right. Each face belongs to one of those pairs. A cuboid has the same three pairs, although its faces need not all be squares of the same size.
2 · Watch
به انگلیسیTake 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.