Question

How many faces does a cuboid have?
(a) 4
(b) 6
(c) 8
(d) None

Answer 1

Hint: In this question, we have to imagine a matchbox in our mind or take a book in our hand and count the number of faces in these objects. The number we will get would be the number of faces a cuboid has because all these objects are of cuboidal shape.

Complete step-by-step answer:

Before proceeding with this question, let us see what cuboid is. In geometry, a cuboid is defined as a convex polyhedron bounded by six quadrilateral faces. We can also say that the faces of the cuboid can be any quadrilateral. Now, we can explain in simpler terms that cuboids are made of 6 rectangles, which are placed at right angles. When we consider objects like a wooden box, a matchbox, a chalk box, a book, etc., we can see that they have a similar shape. All these objects are made of six rectangular planes and thus we can say that the shape of these objects is a cuboid. We also have a shape - cube. The basic difference between a cube and cuboid is that a cube has equal length, height and breadth whereas a cuboid may or may not have the same dimensions of length, height and breadth. The cuboid can also be called a right rectangular prism.
Total surface area of the cuboid \[=2\left[ \left( l\times b \right)\text{+}\left( b\times h \right)+\left( h\times l \right) \right]\]
Volume of the cuboid \[=l\times b\times h\]
where l = length, b = breadth and h = height.
Let us consider the figure for a cuboid as below,

Let us now talk about various parts of cuboid.
Face: It is also called facets or sides. A cuboid has six faces which are all quadrilaterals. We can say that these quadrilaterals are actually rectangles. We can see that each face has four equal sides and all four interior angles are right angles in a rectangular cuboid.
Edge: A line segment formed where two edges meet. Looking at the figure, we can see that the cuboid has 12 edges.
Vertex: A point formed where three edges meet. From the figure, we can see that there are 8 such vertices.
Hence, option (b) is the correct answer.

Note: When we say cuboid, almost everyone imagines a rectangular cuboid but students must note that a rectangular cuboid is not the only cuboid but as we have talked, broadly the faces of the cuboid can be any quadrilateral and are not only limited to rectangles. Also, the number of faces would still be six in any type of cuboid that’s why the answer is correct for all types of cuboids.