Question

How many vertices, faces, and edges does a cuboid have?

Answer 1

Hint: First we will define what a cuboid is. Then we will define the smallest unit of the cuboid that is the rectangle and then we will draw what is a cuboid then we will find out the vertices, faces, and edges of the cuboid and get the answer.

Complete step-by-step solution
First, we will define what a cuboid is. So, a cuboid is a three-dimensional shape with flat rectangular faces and the faces of the cuboid are parallel but not all the faces of a cuboid are equal in dimensions. Now, all angles are right angles and all of its faces are rectangles.
Now, the rectangle is a two-dimensional shape with straight sides where all interior angles are ${90}^{\circ }$ and the opposite sides are parallel and of equal length, which will look like the following figure:
 

Now, let’s see how the cuboid looks, and then we will find out the number of vertices, faces, and edges of the cuboid:

Now, we will see how many faces are there in a cuboid. A cuboid is made up of six rectangles, each of the rectangles is called the face. In the figure above, ABEH, DAHG, DCFG, CBFE, ABCD, and EFGH are the 6 faces of the cuboid. The top face EFGH and bottom face ABCD form a pair of opposite faces. Similarly, ABEH, CDGF, and DAHG, CBEF are pairs of opposite faces. Any two faces other than the opposite faces are called adjacent faces.
Let’s see what is meant by edges. The edge of the cuboid is a line segment between any two adjacent vertices. There are 12 edges, they are AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF, and CD, and the opposite sides of a rectangle are equal. Hence, AD=GH=BC=EF, AH=DH=FC=DG and EH=FG=AB=CD.
Now, we know that the point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid. The given cuboid has 8 vertices A, B, C, D, E, F, G, and H representing the vertices of the cuboid in the given figure.
Hence, the total number of vertices is 8 in a cuboid, the number of edges is 12 and the total number of faces is 6.

Note: One can get confused between a cube and a cuboid, remember that all faces are equal in a cube and the smallest unit is a square and in a cuboid only opposite faces are equal and the smallest unit is a rectangle. Always draw a figure and then count the asked terms carefully.