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Nets and Skeleton Models of Regular Solids

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Octahedron

Source :math.stackexchange.com Fig :combinatorics - Number of unique cycle pa
Source:math.stackexchange.com
Fig:octahedron



  • Each surface is an equilateral triangle .
  • It's a regular solid .
  • It has eight surfaces .





Tetrahedron

Source :www.kidsmathgamesonline.com Fig :Tetrahedron Picture - Images of Shapes
Source:www.kidsmathgamesonline.com
Fig:Tetrahedron



  • Each surface is an equilateral triangle .
  • It's a regular solid .
  • It has four surfaces .




Cube

Source:www.clipartpanda.com
Fig: Cube



  • It's a regular solid and it's also called a regular hexahedron.
  • It has six surfaces .
  • Each surface is square.





Following are the table to know about the number of vertices , edges and faces of some regular polyhedrons :

Regular polyhedron No. of vertices(V) No.of edges (E) No. of face (F) F + V-E
Tetrahedron 4 6 4 4+4-6=2
Hexahedron 8 12 6 6+8-12=2
Octahedron 6 12 8 8+6-12=2

In any regular polyhedron , F+V-E =2 is true. This rule was developed by Swiss Mathematician Euler. It is called Euler's rule.

Cone :

fig: cone
fig: cone




  • It's curved surface meet at a point called it's vertex.
  • It has curved surface with the circular base.
  • It is a solid object.





Cylinder

fig:cylinder
fig:cylinder



  • It has a curved surface with two circular bases .
  • It is a solid object.



  • The cylinder has a curved surface with two circular bases .
  • Cone  has curved surface with the circular base.
  •  Cube has six surfaces .
  • In any regular polyhedron , F+V-E =2 is true. This rule was developed by Swiss Mathematician Eular. It is called Eulr's rule.
.

Questions and Answers

Click on the questions below to reveal the answers

Solution:

Here,
Volume of the box (V) = 1600 cm3 
height of the box = 5 cm
Now,
Volume of the box = Area of its base × height 
∴ Area of its base × 5 = 1600
or, Area of its base × height = 1600 
or, Area of its base = \(\frac{1600}{5}\) 
or, Area of its base = 320 cm2
So, its base covers an area of 320 cm2 on the table.

Solution:

Here,
the surface area of the cubic block = 96 cm2
or, 6 l2 = 96 cm2
or, l2 = \(\frac{96}{6}\) cm2 
or, l= 16 cm
or, l = \(\sqrt{16 cm^2}\)
or, l = 4 cm
∴ The length of its each edge is 4 cm.

Solution:

length of the block (l) = 6 cm 
breadth of the block (b) = 8 cm
 thickness of the block (h) = 4 cm
Now,
Volume of the block = l × b × h 
= 16 cm × 8 cm × 4 cm 
= 512 cm3 
volume of the cube = volume of the block 
or,  l3 = 512 cm3 
or, l = \(\sqrt[3]{512 cm^3}\) 
or, l = 8 cm
Again, 
the surface area of the cube = 6 l2 
= 6 × (8 cm)2 
= 384 cm2 

Solution:

Here,
the volume of water = 3000 l
= 3000 × 1000 cm3
Now,
the volume of the part of the tank containing water = volume of water 
or, Area of its base × height = 3000 × 1000 cm3 
or, 30,000 cm2 × h = 3000 × 1000 cm3
or, h = \(\frac{3000 × 1000 cm^3}{30,000 cm^2}\)
or, h = 100 cm
So, the required height of water level in the tank is 100 cm (or 1 m).

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  • The regular solid is also known as ______ .

    regular skeleton
    regular surface
    regular hexahedron
    regular polyhedron
  • Octahedron has _______ surfaces.

    six
    nine
    seven
    eight
  • Cube has ______ surfaces.

    four
    two
    eight
    six
  • The meeting point of a curved surface is known as ______ .

    edges
    vertex
    segment
    base
  • The line segments that joins any two faces of a regular polyhedron is called its ______ .

    vertex
    edges
    faces
    base
  • Tetrahedron is a ______ solid.

    regular
    same
    irregular
    curved
  • Tetrahedron has ______  number of vertices.

    3
    4
    5
    6
  • Hexahedron has ______  number of edges.

    12
    8
    6
    4
  • Octahedron has ______ number of faces.

    6
    7
    8
    10
  • Tetrahedron has ______ surfaces.

    three
    five
    four
    six
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