# 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.

# 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.

# Inscribed and circumscribed solids

• If a sphere of the maximum volume is inscribed in a cube of edge â€˜aâ€™, then the radius of the sphere =
• If a cube of the maximum volume is inscribed in a sphere of radius â€˜râ€™, then the edge of the cube

• If a cube of the maximum volume is inscribed in a hemisphere of radius â€˜râ€™, then the edge of the cube Ã— 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.