The table shows information about the faces, edges and vertices for some prisms.
Write a formula that connects the number of sides of the end face,
S with the number of vertices, V
Hence, find the number of vertices of a prism whose cross-section is a 60-sided polygon.
Answers
Given : information about the faces, edges and vertices for some prisms.
To Find : a formula that connects the number of sides of the end face,
S with the number of vertices, V
number of vertices of a prism whose cross-section is a 60-sided polygon.
Solution:
information about the faces, edges and vertices for some prisms.
Shape Faces Edges Vertices
Triangle (3) 5 9 6
rectangle(4) 6 12 8
Pentagon(5) 7 15 10
Hexagon (6) 8 18 12
Shape Faces Edges Vertices
Triangle (3) 3+2= 5 3 * 3 = 9 3 * 2 = 6
rectangle(4) 4+2= 6 4 * 3 = 12 4 * 2 = 8
Pentagon(5) 5+2= 7 5 * 3 = 15 5 * 2 = 10
Hexagon (6) 6 + 2 =8 6 * 3 = 18 6 * 2 = 12
n sides n + 2 3n 2n
Faces = number of sides + 2
Edges = 3 * number of sides
Vertices = 2 * number of sides
V = 2S
Faces + Vertices = Edges + 2 ( Euler formula )
Number of vertices of a prism whose cross-section is a 60-sided polygon.
= 2 * 60
= 120
120 vertices
Shape Faces Edges Vertices
60 sides 62 180 120
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