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Tetrahedron

A tetrahedron is a solid which has 4 faces. All the faces of a tetrahedron are equilateral triangles. A tetrahedron has 4 vertices and 6 edges.

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Octahedron

An octahedron is a solid which has 8 faces. All the faces of an octahedron are equilateral triangles. An octahedron has 6 vertices and 12 edges.
 
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Inscribed and circumscribed solids

  • If a sphere of the maximum volume is inscribed in a cube of edge ‘a’, then the radius of the sphere = Description: 2343.png
  • If a cube of the maximum volume is inscribed in a sphere of radius ‘r’, then the edge of the cube
     
    Description: 2352.png
  • If a cube of the maximum volume is inscribed in a hemisphere of radius ‘r’, then the edge of the cubeDescription: 2361.png × r

Some important deductions

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If a cone is made by a sector of a circle (AOBD), then the following two things must be remembered
  • The area of the sector of a circle (AOBD) = The CSA of the cone
  • Radius of the cirlce (r) = Slant height (l) of the cone.




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