SOLUTION: Use Euler's formula to answer the question.
A polyhedron has 15 vertices and 31 edges. How many faces does it have?
(I know that the formula is v+f=E+2, would I just subtract
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-> SOLUTION: Use Euler's formula to answer the question.
A polyhedron has 15 vertices and 31 edges. How many faces does it have?
(I know that the formula is v+f=E+2, would I just subtract
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Question 204158: Use Euler's formula to answer the question.
A polyhedron has 15 vertices and 31 edges. How many faces does it have?
(I know that the formula is v+f=E+2, would I just subtract 33 from 15 to get the correct number of faces?)
Thank you so much for your help on this problem... Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! euler's formula states that:
V - E + F = 2
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if the polyhedron has 15 vertices and 31 edges, simply plug into the formula to get your answer.
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V - E + F = 2 becomes:
15 - 31 + F = 2 which becomes:
-16 + F = 2 which becomes:
F = 18
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plug back into Euler's formula to check:
15 - 31 + 18 = 2
-16 + 18 = 2
2 = 2
this is good
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you stated the equation as V + F = E + 2 which looks ok.
V = 15
E = 31
plug into your equation to get:
15 + F = 31 + 2
this gets you:
F = 31 - 15 + 2
which means you would subtract 15 from 31 as you stated and add it to 2 in order to get your answer.
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you just need to substitute into the euler equation and you'll get your answer easily.
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you have to move things around but that's normal arithmetic.
15 + F = 31 + 2
subtract 15 from both sides of the equation to get:
F = 31 - 15 + 2
combine like terms to get:
F = 16 + 2 = 18
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