FIND THE SOLUTION USING EULERS FORMULA. CAN A POLIHYDRON HAVE 20 FACES, 30 EDGES AND 12 VERTICES PROVE BY EULERS FORMULA
Answers
Step-by-step explanation:
As per question:
Euler's Formula is for any polyhedrons. i.e.
F + V - E = 2
Given, F = 20 and V = 12 and E = a
According to the formula:
20 + 12 - a= 2
32 - a = 2
a = 32 - 2
a = 30
Step-by-step explanation:
Given:−
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The polyhedron has 20 faces, 30 edges and 12 vertices.
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\sf\underline{\red{\:\:\: Need\:To\: Prove:-\:\:\:}}
NeedToProve:−
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We need to prove this statement by using Euler's formula.
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\sf\underline{\red{\:\:\:Proof:-\:\:\:}}
Proof:−
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Here in this question we are given with the faces, edges of polyhedron as well as vertices of polygon respectively. That is,
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\begin{gathered}\frak{Here}\begin{cases}\sf{\:\;\; F = 20}\\\\\sf{\;\;\; V = 12}\\\\\sf{\;\;\; E = \: 30}\end{cases}\end{gathered}
Here
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F=20
V=12
E=30
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We know that if we are given with the faces, edge & vertices of polyhedron, we have the required formula, that is,
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\sf{:\implies V - E + F = 2}:⟹V−E+F=2 ⠀
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⠀⠀⠀⠀ Here V is the vertices of polyhedron, E is the number edge and F is the Faces of polyhedron, And here in this question we have V = 12, E = 30 and F = 20. So by using the Euler's polyhedron formula we can easily proof.
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By using the formula and substituting all the given values in the formula, we get:
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\sf{:\implies 12 - 30 + 20 = 2}:⟹12−30+20=2
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\sf{:\implies -18 + 20 = 2}:⟹−18+20=2
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\sf{:\implies \blue{\boxed{\pmb{\bf{ \pink{2 = 2}}}}}}:⟹
2=2
2=2
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Therefore, this statement is true