3-D Objects

Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 3.0 Geometry | Sub-Strand 3.3 3-D Objects (6 Lessons)

Lesson objectives

By the end of this topic, you will be able to:

• Identify vertices, faces, and edges in cuboids and cubes
• Identify faces and edges of cylinders
• Describe plane figures found in 3-D objects
• Appreciate the use of 3-D objects in real life

3-D Objects

A flat shape has length and width. A 3-D object has length, width and height as well. It takes up space.

a) The three words

A face is a flat surface you could put your hand on.

An edge is the line where two faces meet.

A vertex is a corner where edges meet. More than one is called vertices.

b) Cubes and cuboids

Object	Faces	Edges	Vertices
Cube	6	12	8
Cuboid	6	12	8

A cube has six faces and every one is a square. All its edges are the same length.

A cuboid also has six faces, but they are rectangles. Opposite faces match each other.

Both have the same counts. What differs is the shape of the faces.

Count them on a real box. Touch each face, run a finger along each edge, and press each corner.

c) Cylinders

A cylinder has three faces. Two are flat circles, at the top and the bottom. One is curved and wraps round the side.

It has two edges, where the curved surface meets each circle.

It has no vertices at all, because there are no corners.

A tin of tomatoes is a cylinder. So is a drum and a round pencil.

d) Flat shapes inside solid ones

Every 3-D object is built from flat shapes.

Object	Flat shapes in it
Cube	squares
Cuboid	rectangles
Cylinder	circles
Triangular prism	triangles and rectangles
Square pyramid	a square and triangles

e) Opening a solid out

Cut along some edges and a box opens out flat. That flat shape is its net.

Every face appears once in the net.

Fold it back up and you have the solid again. Try it with an empty packet.

f) Where this is used

A packaging maker designs boxes. A builder stacks blocks. A shopkeeper fills a shelf. Any container you have ever opened was once a net.

Words to know

• Vertex (plural: vertices) — a corner point where edges meet.
• Face — a flat (or curved) surface of a 3-D object.
• Edge — a line where two faces meet.
• Plane figure — a flat, two-dimensional shape (e.g. square, rectangle, circle).

:::checkpoint Check yourself

1. How many faces, edges and vertices does a cube have?
2. Why does a cylinder have no vertices?
3. What flat shape is found in a cuboid?
4. What is a net? :::

Bridge to practice

Try the exercises below — counting vertices, faces, and edges for cubes, cuboids, and cylinders, and identifying the plane figures on their surfaces.