Question

A solid has $10$ faces and $15$edges. How many vertices does it have?

Answer 1

Given that,

Faces = $10$

Edges = $15$

By using Euler's formula,

$$\begin{gathered} V+F-E=2 \\ V+10-15=2 \\ V-5=2 \\ V=5+2 \\ V=7 \end{gathered}$$

Hence, number of vertices this solid has $7$.