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Octahedron
Tetrahedron
Cube
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 :
Cylinder
Solution:
Here,
Volume of the box (V) = 1600 cm^{3}
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 cm^{2}
So, its base covers an area of 320 cm^{2} on the table.
Solution:
Here,
the surface area of the cubic block = 96 cm^{2}
or, 6 l2 = 96 cm^{2}
or, l^{2} = \(\frac{96}{6}\) cm^{2}^{ }
or, l^{2 }= 16 cm^{2 }
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 cm^{3}
volume of the cube = volume of the block
or, l^{3} = 512 cm^{3}
or, l = \(\sqrt[3]{512 cm^3}\)
or, l = 8 cm
Again,
the surface area of the cube = 6 l^{2}
= 6 × (8 cm)^{2}
= 384 cm^{2}
Solution:
Here,
the volume of water = 3000 l
= 3000 × 1000 cm^{3}
Now,
the volume of the part of the tank containing water = volume of water
or, Area of its base × height = 3000 × 1000 cm^{3}
or, 30,000 cm^{2} × h = 3000 × 1000 cm^{3}
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).
The regular solid is also known as ______ .
Octahedron has _______ surfaces.
Cube has ______ surfaces.
The meeting point of a curved surface is known as ______ .
The line segments that joins any two faces of a regular polyhedron is called its ______ .
Tetrahedron is a ______ solid.
Tetrahedron has ______ number of vertices.
Hexahedron has ______ number of edges.
Octahedron has ______ number of faces.
Tetrahedron has ______ surfaces.
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