Answered

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A solid has 8 faces and 12 edges. How many vertices does this solid have?

A. 4
B. 6
C. 8
D. 10

Please select the best answer from the choices provided:

A.
B.
C.
D.

Sagot :

GinnyAnswer
To determine the number of vertices for the given solid, we can use Euler's formula for polyhedra. Euler's formula states:

[tex]\[ V - E + F = 2 \][/tex]

where:
- [tex]\( V \)[/tex] represents the number of vertices,
- [tex]\( E \)[/tex] represents the number of edges,
- [tex]\( F \)[/tex] represents the number of faces.

Given:
- [tex]\( F = 8 \)[/tex] (the solid has 8 faces),
- [tex]\( E = 12 \)[/tex] (the solid has 12 edges).

We need to find [tex]\( V \)[/tex]. Using Euler's formula, we rearrange it to solve for [tex]\( V \)[/tex]:

[tex]\[ V = E - F + 2 \][/tex]

Now, substitute the given values into the equation:

[tex]\[ V = 12 - 8 + 2 \][/tex]

Perform the arithmetic:

[tex]\[ V = 4 + 2 \][/tex]
[tex]\[ V = 6 \][/tex]

Thus, the solid has 6 vertices. Therefore, the correct answer is:

B. 6
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