Find whether the following table satisfies the EULER-S formula or not- -4 MARKS- begin array - c - c - Whine No- of - Faces - No- of - Vertices - No- of Edges lilhline 3 - 4 - 6 Wline3 - 8 - 12 Wlhline4 - 6 - 12 Wlhline3 - 20 - 30 Wllhline5 - 12 - 30 wlhlinelend array

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Standard VII

Mathematics

Faces, Edges and Vertices

Find whether ...

Question

Find whether the following table satisfies the EULER'S formula or not. [4 MARKS]

$\begin{matrix} N o . o f F a c e s & N o . o f V e r t i c e s & N o . o f E d g e s 3 & 4 & 6 3 & 8 & 12 4 & 6 & 12 3 & 20 & 30 5 & 12 & 30 \end{matrix}$

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Solution

Formula: 1.5 Marks
Application: 0.5 Mark each

Euler’s Formula:
Faces + Vertices – Edges = 2
1) 3 + 4 - 6 = 1

1 $\neq$ 2

2) 3 + 8 -12 = -1

1 $\neq$ 2

3) 4 + 6 - 12 = -2

-2 $\neq$ 2

4) 3 + 20 - 30 = -7

-7 $\neq$ 2

5) 5 + 12 - 30 = -13

-13 $\neq$ 2

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Find whether the following table satisfies the EULER'S formula or not. [4 MARKS] No. of FacesNo. of VerticesNo. of Edges346381246123203051230

Formula: 1.5 Marks Application: 0.5 Mark each Euler’s Formula: Faces + Vertices – Edges = 2 1) 3 + 4 - 6 = 1 1 ≠ 2 2) 3 + 8 -12 = -1 1 ≠ 2 3) 4 + 6 - 12 = -2 -2 ≠ 2 4) 3 + 20 - 30 = -7 -7 ≠ 2 5) 5 + 12 - 30 = -13 -13 ≠ 2

Find whether the following table satisfies the EULER'S formula or not. [4 MARKS]

$\begin{matrix} N o . o f F a c e s & N o . o f V e r t i c e s & N o . o f E d g e s 3 & 4 & 6 3 & 8 & 12 4 & 6 & 12 3 & 20 & 30 5 & 12 & 30 \end{matrix}$

Formula: 1.5 Marks
Application: 0.5 Mark each

Euler’s Formula:
Faces + Vertices – Edges = 2
1) 3 + 4 - 6 = 1

1 $\neq$ 2

2) 3 + 8 -12 = -1

1 $\neq$ 2

3) 4 + 6 - 12 = -2

-2 $\neq$ 2

4) 3 + 20 - 30 = -7

-7 $\neq$ 2

5) 5 + 12 - 30 = -13

-13 $\neq$ 2