Mathematics
Verify Euler's formula for the following three dimensional figures :
(i)
(ii)
(iii)
3D in 2D
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Answer
(i)
Given:
F = 8, V = 6 , E = 12
According to Euler's formula,
F + V - E = 2
So, LHS:
⇒ 8 + 6 - 12
⇒ 14 - 12
⇒ 2
Thus, LHS = RHS
Hence, Euler's formula is verified.
(ii)
Given:
F = 9, V = 9 , E = 16
According to Euler's formula,
F + V - E = 2
So, LHS:
⇒ 9 + 9 - 16
⇒ 18 - 16
⇒ 2
Thus, LHS = RHS
Hence, Euler's formula is verified.
(iii)
Given:
F = 7, V = 10 , E = 15
According to Euler's formula,
F + V - E = 2
So, LHS:
⇒ 7 + 10 - 15
⇒ 17 - 15
⇒ 2
Thus, LHS = RHS
Hence, Euler's formula is verified.
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