28 VSA | Single Observe the given figure and answer the questions given below. Find the number of vertices in the given 3D structure. 17 18 20 21
ans???
Answers
Answer:
If l is the length, b is the breadth and h is the height of the cuboid, then the sum of areas of six rectangles of a cuboid gives the total surface area of the cuboid. The formula for it is given below.
Total surface area of a cuboid = 2 [( l × b ) + ( l× h ) + ( b× h )]
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Answer:
Correct option is A)
1.Here,
No. of Faces (F):5
No. of Vertices (V):6
No. of Edges (E):9
Euler’s formula: F + V = E + 2
⇒ 5 + 6 = 9 + 2
⇒ 11 = 11
∴ Euler’s formula satisfies for the shape.
2.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
3.Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
4.Here,
No. of Faces (F):6
No. of Vertices (V):6
No. of Edges (E):10
Euler’s formula: F + V = E + 2
⇒ 6 + 6 = 10 + 2
⇒ 12 = 12
∴ Euler’s formula satisfies for the shape.
5.Here,
No. of Faces (F):5
No. of Vertices (V):5
No. of Edges (E):8
Euler’s formula: F + V = E + 2
⇒ 5 + 5 = 8 + 2
⇒ 10 = 10
∴ Euler’s formula satisfies for the shape.
6.Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
7.Here,
No. of Faces (F):8
No. of Vertices (V):6
No. of Edges (E):12
Euler’s formula: F + V = E + 2
⇒ 8 + 6 = 12 + 2
⇒ 14 = 14
∴ Euler’s formula satisfies for the shape.
8.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.