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Year 8 Interactive Maths - Second Edition


Pyramid and Spheres

Pyramids are polyhedra because they are made up of plane facesSpheres are not polyhedra because they are curved.


Pyramids

If a line that is fixed at a point, called the vertex, is moved around the perimeter of a polygon, then a pyramid is formed.

The following solid is pyramid.

Pyramids are named after their base.  So, the pyramid shown above is an example of a rectangular pyramid.

Some other pyramids are shown below.

A pyramid is said to be right when its vertex is directly above the centre of the base.  The cross-sections parallel to the base are the same shape but have different sizes.


The net of the above pyramid consists of:

  • a rectangular base; and
  • four triangular faces

Note:
  • The cross-sections parallel to the base have the same shape as the base but different sizes.
  • The net of a pyramid consists of a base polygon and a number of triangular faces.
  • A regular pyramid has a base that is a regular polygon and has faces which are isosceles triangles.


Spheres

If a semicircle is revolved about its diameter, then a sphere is formed.

The following solid is a sphere.

The cross-sections of a sphere are circles.  The cross-sections that pass through the centre of the sphere are called great circles whilst other cross-sections are called small circles.

A hemisphere is a half sphere.

 

 

 



Key Terms

pyramid, vertex of a pyramid, base of a pyramid, rectangular pyramid, triangular pyramid, hexagonal pyramid, octagonal pyramid, right pyramid, net of a pyramid, regular pyramid, sphere, centre of a sphere, great circles of a sphere, small circles of a sphere, hemisphere


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