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Shape, Space and Measure (Intermediate) - 3D objects, Nets and the Circle
 
3D Objects | Nets | Circle
3D Objects

The names of the different parts of an object are:

Faces - These are the flat surfaces
Vertices - Are the corners (vertex for one)
Edges - 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.
 
Object Vertices Faces Edges
Cuboid 8 6 12
Triangular Prism 6 5 9
Pyramid 5 5 8
 
 
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.
 
3d3nets
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 = 12m
2) If d=18cm, calculate the radius
18 = 2 x r
r = 9cm