FRUSTUM OF A CONE

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Frustum is a Latin word meaning 'piece cut off', and its plural is 'frusta'.

 A frustum is a portion of a solid that lie between one or two parallel planes.
  • The frustum of cone has two circular ends with different radii.

Take a right circular cone and remove a portion of it. There are many ways in which we can do this. But one particular case that we are interested in it is the removal of a smaller right circular cone by cutting the given cone by a plane parallel to its base.

You must have observed that the glasses ( tumblers ), in general, used for drinking water, are of this shape.


FRUSTUM OF A CONE

FRUSTUM OF A CONEConstruction of frustum of cone


  • Take some clay, or any other such material ( like plasticine, etc. ) and form a cone. 
  • Cut it with a knife parallel to its base. 
  • Remove the cone that is formed on one side of that plane.
  • The part that now left is a frustum of cone.
  • The frustum of cone has two circular ends with different radii.


Let h be the height, l the slant height and the radii of the ends of the frustum of the cone shown in figure. 

 Then the volume, surface area and the curved surface area can be calculated as follows:
FRUSTUM OF A CONE

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