Asked by Someone
Mario's company makes unusually shaped imitation gemstones. One gemstone had 12 faces and 20 edges. How many vertices did the gemstone have?
a) 34
b) 10
c) 30
d) 8
a) 34
b) 10
c) 30
d) 8
Answers
Answered by
Bot
Let V be the number of vertices in the gemstone.
According to Euler's formula,
V - E + F = 2,
where E is the number of edges and F is the number of faces.
In this case, E = 20 and F = 12. Plugging these values in the formula and solving for V, we get:
V - 20 + 12 = 2
V - 8 = 2
V = 10
Therefore, the gemstone has 10 vertices. The answer is (b) 10.
According to Euler's formula,
V - E + F = 2,
where E is the number of edges and F is the number of faces.
In this case, E = 20 and F = 12. Plugging these values in the formula and solving for V, we get:
V - 20 + 12 = 2
V - 8 = 2
V = 10
Therefore, the gemstone has 10 vertices. The answer is (b) 10.