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OlgaM077 [116]
2 years ago
11

Manuel y Carlos encuentran un libro de matemática usado y en una de las hojas se observa la figura de un poliedro demasiado borr

osa, pero se ven algunos datos sobre él que dicen: El poliedro tiene 12 aristas y la suma de su número de caras con su número de vértices es 14. Manuel afirma que se trata de un dodecaedro y Carlos dice que es un cubo. ¿Quién de ellos tiene la razón?
Mathematics
1 answer:
Sergio039 [100]2 years ago
3 0

Answer:

Carlos tiene razón. El poliedro es un cubo.

Step-by-step explanation:

Comencemos analizando el número de caras del dodecaedro y del cubo.

El dodecaedro está conformado por 12 caras.

El cubo en cambio, está conformado por 6 caras.

En cuanto a aristas el dodecaedro tiene 30 aristas y en cambio el cubo tiene 12. Por ende, descartamos la idea de que el poliedro sea un dodecaedro.

Finalmente en cuanto a vértices, el dodecaedro tiene 20 vértices y el cubo tiene 8 vértices.

Si sumamos el número de caras y el número de vértices en el cubo obtenemos :

6 + 8 = 14

Con esto, verificamos que la figura borrosa es de un cubo y que Carlos tiene razón.

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