Answered

4.
d)
A
R
B
D
UNIT
2
по
Identify the names of the following solid objects and write down the
of faces, edges and vertices. Also, establish the relation F +V-E=2,
E, V and F have their usual meaning.
a)
d)
b)
Devnagari and Hindu-arabic
numbers
Study the place value
of numbers (Upto
Crores)
The Smallest and Greatest
Number Upto 7 Digits
Rounding Off
Addition with/without
carrying
• Verbal probelms on
addition
• Subtraction with/without
borrowing
• Verbal probelms on
•
subtraction
Multiplication with three/
four digit number
Division

Verified Answer :

GinnyAnswer

Certainly! To identify the names of solid objects and to calculate their faces, edges, vertices, and verify the Euler's formula \(\( F + V - E = 2 \)\), you need to understand the individual properties of each solid. Let's look at some common examples:

a) Cube (or Regular Hexahedron)

- Faces (F): A cube has 6 faces. Each face is a square.
- Edges (E): A cube has 12 edges.
- Vertices (V): A cube has 8 vertices.
- Verification of Euler's formula: \(\( F + V - E = 6 + 8 - 12 = 2 \)\).

b) Tetrahedron

- Faces (F): A tetrahedron has 4 faces. Each face is a triangle.
- Edges (E): A tetrahedron has 6 edges.
- Vertices (V): A tetrahedron has 4 vertices.
- Verification of Euler's formula: \(\( F + V - E = 4 + 4 - 6 = 2 \)\).

c) Octahedron

- Faces (F): An octahedron has 8 faces. Each face is an equilateral triangle.
- Edges (E): An octahedron has 12 edges.
- Vertices (V): An octahedron has 6 vertices.
- Verification of Euler's formula: \(\( F + V - E = 8 + 6 - 12 = 2 \)\).

d) Dodecahedron

- Faces (F): A dodecahedron has 12 faces. Each face is a regular pentagon.
- Edges (E): A dodecahedron has 30 edges.
- Vertices (V): A dodecahedron has 20 vertices.
- Verification of Euler's formula: \(\( F + V - E = 12 + 20 - 30 = 2 \)\).

Each polyhedron description includes:
1. Name: The specific solid we're examining.
2. Faces, Edges, and Vertices: Defined by counting the respective elements.
3. Verification: Ensuring that Euler's formula \(\( F + V - E = 2 \)\) holds true for the solid.

One can use these principles to establish and confirm the properties for other solid objects. If you encounter a new or different polyhedron, remember to count the faces, edges, and vertices, and apply Euler's formula to verify the consistency of these properties.

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