Question

Draw a diagram to represent a cuboid. Label its vertices as P, Q, R, S, T, U, V and W. Now write the name of its faces and edges.

Answer 1

Hint: Try to recall the different examples of things which are cuboidal in shape and we use in our day today life, for example: pencil box, laptops etc. Also, remember that the cuboid has six faces and 12 edges. So, draw the diagram accordingly and name its vertices as given in the question.

Complete step-by-step answer:
Let us start the solution by knowing the structural property of a cuboid and drawing a representative diagram of it. In mathematics, the word cuboid refers to a polyhedron which consists of rectangles as its faces.
Now let us draw a diagram for better visualisation.
      

Now, let us first write the names of all its edges. The edges of the above cuboid are: PT, PS, PQ, SR, SW, RQ, RV, QU, TW, TU, UV, VW. Also, from these we can conclude that the cuboid has 12 edges.
Now we will write the names of its faces. The faces of a cuboid are rectangular in shape, with pairs of opposite faces having the same dimensions and area. A cuboid has six faces in total. The faces of the above cuboid are: PQRS, TUVW, QRVU, QPTU, PSWT, SRVW.

Note: Be careful while reporting the names of the faces, as the order of naming the face must be cyclic, i.e., the face SRVW cannot be written as SVRW. It is also a good practice to remember the relation between the number of faces, edges and vertices of a polyhedron, i.e., the sum of the number of faces and vertices is equal to 2 more than the number of edges.