SAT II Math II : Other 3-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #41 : 3 Dimensional Geometry

A convex polyhedron has twenty faces and thirty-six vertices. How many edges does it have?

Possible Answers:

\(\displaystyle 54\)

\(\displaystyle 18\)

\(\displaystyle 52\)

\(\displaystyle 16\)

\(\displaystyle 56\)

Correct answer:

\(\displaystyle 54\)

Explanation:

The number of vertices \(\displaystyle V\), edges \(\displaystyle E\), and faces \(\displaystyle F\) of any convex polyhedron are related by By Euler's Formula:

\(\displaystyle V- E + F = 2\)

Setting \(\displaystyle V= 36, F = 20\) and solving for \(\displaystyle E\):

\(\displaystyle 36- E + 20 = 2\)

\(\displaystyle 56- E = 2\)

\(\displaystyle E = 54\)

The polyhedron has 54 edges.

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