3D Shapes

1Summary 重點摘要

3D shapes are solid and take up space.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Flat and solidA sheet of paper has only one flat face; it is a flat shape. A block has thickness and takes up space; it is a solid shape. Example: a square sheet of paper is flat with 1 face, while a die is solid with 6 faces. A solid can be picked up and turned, and any of its faces can rest on the desk; a flat shape only lies on the paper. A common mistake is taking the drawing of a solid on paper for a real solid, yet it is only a picture; the key is whether the thing has thickness and can stand steadily.
2. Step 2: SphereA sphere has a curved surface all over, with no flat face at all, so it keeps rolling on a slope. Example: a ping-pong ball is a sphere; placed on a sloping desk it rolls right off, and balls and melons are spheres too. Why can a sphere not stand still? Because it has no flat face at all to be its base. A common mistake is mixing up the circle and the sphere: a circle is a flat shape while a sphere is a solid, a circle is like the shadow of a sphere, and only the touchable object is a sphere.
3. Step 3: CylinderA cylinder has one circular flat face on top and one circular flat face below, the two circles being the same size, while its side is a curved surface. Example: a soup can is a cylinder; standing upright it rests steadily because a flat face serves as its base, but lying down it rolls because the curved side touches the desk. A common mistake is thinking a cylinder can never roll; in fact it is steady upright and rolls lying down, and both behaviours are its features. Count them: it has 2 flat faces and 1 curved surface.
4. Step 4: CuboidA cuboid has 6 faces, and every face is a rectangle, like a thick book. Example: a dictionary is a cuboid; count face by face: top, bottom, front, back, left and right, 6 rectangular faces in all, and opposite faces match each other in shape and size. A common mistake is missing the bottom or the back when counting faces, because they cannot be seen; pick the box up and turn it round to count them all. Press a finger on each face you have counted, and nothing will be repeated or left out.
5. Step 5: CubeA cube also has 6 faces, and its special feature is that all 6 faces are exactly the same size, each one a square. Example: a die is a cube, and it rests steadily on any face because every face is the same square. A cube can be seen as one kind of cuboid: when the length, width and height of a cuboid are all equal, it becomes a cube. A common mistake is thinking cubes and cuboids are entirely different kinds, yet a cube is a special cuboid; also remember it has 6 faces, while 12 is the number of its edges, so do not mix them up.
6. Step 6: ConeA cone has one circular flat face at the bottom and narrows as it goes up, ending in one pointed tip at the top, so it has only 1 flat face. Example: a party hat is a cone; turn it upside down and the round base and the point can both be seen, and funnels and ice-cream cones are cones too. Why does a cone not have a flat face at both ends like a cylinder? Because the top narrows into a single point. A common mistake is mixing up the cone and the cylinder; remember, a cylinder has 2 circular faces while a cone has only 1 and a sharp tip.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Solids have thickness and take up space.
• Sphere: no flat faces, it rolls.
• Cylinder: 2 round faces + a curved side.
• Cuboid has 6 faces; cube has 6 square faces.
• Cone: 1 round face + 1 point.