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InterviewSolution
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Verify Euler’s formula for the table given belowS. No.FacesVerticesEdges(i)446(ii)10612(iii)122030(iv)201330(v)326090 |
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Answer» Euler’s formula is given by F + V – E (i) F = 4 ; V = 4; E = 6 F + V – E = 4 + 4 – 6 = 8 – 6 F + V – E = 2 ∴ Euler’s formula is satisfied. (ii) F = 10; V = 6; E = 12 F + V – E = 10 + 6 – 12 = 16 – 12 = 4 ≠ 2 ∴ Euler’s formula is not satisfied. (iii) F = 12 ; V = 20 ; E = 30 F + V – E = 12 + 20 – 30 = 32 – 30 = 2 ∴ Euler’s formula is satisfied. (iv) F = 20 ; V = 13 ; E = 30 F + V – E = 20 + 13 – 30 = 33 – 30 = 3 ≠ 2 ∴ Euler’s formula is not satisfied. (v) F = 32 ; V = 60 ; E = 90 F + V – E = 32 + 60 – 90 = 92 – 90 = 2 ∴ Euler’s formula is satisfied. |
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