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Year 8 Interactive Maths - Second Edition


Cones and Cylinders

Cones and cylinders have curved surfaces as shown below.  So, they are not prisms or polyhedra.


Cones

If one end of a line is rotated about a second fixed line while keeping the line's other end fixed, then a cone is formed.  The point about which the line is rotated is called the vertex and the base of the cone is a circle.

A cone is said to be right when the vertex is directly above the centre of the base.


The net of a three-dimensional object is a representation of its faces in two dimensions.

The net of a cone consists of the following two parts:

  • a circle that gives the base; and
  • a sector that gives the curved surface


Cylinders

If a line is rotated about a second fixed line while keeping both lines parallel, then a cylinder is formed.


Note:
  • The fixed line about which the line is rotated is called the axis of symmetry.
  • The base of the cylinder is a circle and the top of the cylinder is also a circle.
  • A cylinder is said to be right when the line joining the centre of the base and the centre of the top is perpendicular to the base of the cylinder.
  • The cross-sections parallel to the base are circles and are all identical.


The net of a cylinder consists of three parts:

  • One circle gives the base and another circle gives the top.
  • A rectangle gives the curved surface.


Key Terms

cones, vertex of a cone, right cone, nets, net of a cone, cylinders, cylinder's axis of symmetry, right cylinder, net of a cylinder


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