84
Cuboids and cubes
Textbook: Part 3, lesson 84, pp. 51–53
GoalCuboids and cubes: faces, edges and vertices; how they are alike and different.
New words
cube · kubface · yoqedge · qirravertex (corner) · uch
Explanation
A cuboid and a cube both have 6 faces, 12 edges and 8 vertices. The faces of a cuboid are rectangles; opposite faces are equal. Its 12 edges fall into three groups (length, width, height) with 4 equal edges in each. All faces of a cube are equal squares and all 12 edges are equal. So a cube can be called a special kind of cuboid.
Worked examples
A matchbox is a cuboid: 6 faces, 12 edges, 8 vertices.
A die is a cube: 6 identical square faces and 12 equal edges.
Class activity
“Guess the solid”: a bag holds a cube, a cuboid, a sphere and a cylinder. A child feels one without looking, counts faces and edges, and names it.
Practice
1
What is the sum of the number of faces and the number of edges of a cube?
18
2
How many vertices does a cuboid have?
8
3
A cuboid is 9 dm long, 3 dm wide and 6 dm high. How many of its edges are 9 dm long?
4
4
In a cuboid whose length, width and height are all different, how many groups of edges of different lengths are there?
3
5
Can a cube be called a kind of cuboid?
Yes: a cube is a cuboid with all edges equal.