Question

Apply Euler's formula for a solid that has 16 faces and 21 edges. How many vertices does it have?

• A. $3$
• B. $5$
• C. $7$
• D. $9$

Answer 1

Answer: (C)

$7$

We know that, Euler's polyhedron formula is $V-E+F=2$
where, $V$ is the number of vertices
$E$ is the number of edges
$F$ is the number of faces

Here, $E=16,F=21$

Hence, $V-21+16=2$

$\Rightarrow V-5=2$
$\Rightarrow V=7$

Hence, the solid has $7$ vertices.