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3D Objects, Nets and the Circle

3D Objects

The names of the different parts of an object are:

Faces – These are the flat surfaces.
Vertices – These are the corners (vertex for one).
Edges – These are the sides of the faces.

These are shown in the diagram below, for different objects.

3d1nets

Note: For all these there is a formula connecting number of faces (F), edges (E), and vertices (V). The numbers can be seen in the table below.

Check that this formula works:

V + F = E + 2

Drawing 3D objects on plain or isometric paper should be practiced.

Nets

The net of a 3D object is a drawing of the object, ‘flattened out’, showing all the faces.

For example: The net of a cuboid:

3d2nets

This can be drawn in a number of ways. To check, it must fold up without any overlaps.

Two nets of the cuboid are shown above. Can you think of more?

Circle

The following diagram shows all the parts of the circle, labelled. These parts of the circle need to be learned and are tested in the exam.

Key:

Radius (r)

Centre (O)

Circumference (C)

Diameter (d)

Sector – Area between 2 radii.

Arc - Part of the circumference.

Chord – Line from one point on the circumference to another.

Segment – Area cut off by a chord.

Tangent – Straight line from a point (P) outside the circle touching it at one point only (Q).

Note: The diameter is twice the radius.

d = 2r

For example:

1) If r = 6m, calculate the diameter.

d = 2 x 6 = 12 m

2) If d = 18cm, calculate the radius.

18 = 2 x r
r = 9 cm