Question

Find the number of faces, vertices and edges of a cube

Answer 1

Hint: To solve the problem of finding the number of faces, vertices or edges of a solid shape, we convert the solid shape into a net pattern. So, in case of a cube, we get the following net drawing (as shown)

Complete step-by-step answer:

After we have drawn the net figure, it becomes very easy to evaluate the number of faces, vertices and edges of a cube.

Before we begin the calculation, we understand few definitions which would be helpful in solving the above problem

Face is a 2-D shape that makes up one of the surfaces of solid shape. In this case, the faces on the net pattern are coloured blue for the sake of convenience.

 A vertex is the corner that is formed where the ends of the line segments of two or more faces meet. In simple terms, these are the points where various line segments meet. (in the net pattern of the solid shape).

Edges are simply the line segments where two faces of a solid shape meet. In the above net pattern of the cube, we can see the edges highlighted in black.

Now, we can easily calculate the number of faces, vertices and edges.

Clearly, number of faces are 6 (since, six faces are highlighted blue on the net pattern according to the definition)

Further, we can see that line segments meet on 8 points on the net pattern of the cube. Thus, there are 8 vertices.

Similarly, we see that the number of edges are 12. (12 edges are highlighted black on the net pattern based on the definition)

Note: An alternative method to do this problem is based on Euler’s formula, which states that-

F+V-E=2 (where, F=number of faces; V=number of vertices; E=number of edges)

Thus, if we have information about the number of faces and vertices, we can calculate the number of edges with the help of this formula. Example, in this case, F=6, V=12

Thus, 6+8-E=2

E=14-2=12