Question

Which amongst the following is not a polyhedron?
A.

B.

C.

D.

Answer 1

Hint: To solve this question, we will take the reference of the definition of a polyhedron to choose the correct option. We should note that a polyhedron is a 3-dimensional solid, that has flat surfaces and is joined at their edges.

Complete step-by-step answer:

In the question, we have been given four options of figures A, B, C, and D and have been asked to find out which among them is not a polyhedron. So, we will look at the definition of a polyhedron first. A polyhedron is a 3-dimensional solid which consists of a collection of polygons that are usually joined at their edges and have flat surfaces. So, we will check out all the options individually if they satisfy this basic definition of polyhedron. So, if any of the options have flat surfaces and are joined at their edges, then they would be considered as polyhedrons. So, let us consider each option one by one.
Option A.

The given figure can be understood as a cube. If we look at the figure in this option, we can make out that it is a solid with flat faces and are joined at its edges. It is an example of a regular polyhedron. So, we can say that a cube is a polyhedron.
Option B.

Now, coming to option B, we can understand that the given figure is a pentagonal prism. Prism is a type of polyhedron. It has pentagonal base on either ends and has 5 flat faces joining the bases at edges. So, we can conclude that pentagonal prism is also a polyhedron.
Option C.

The figure shows a tetrahedron. Now, we know that tetrahedron has all its faces flat and identical. It is clear from the figure that the flat faces are joined at the edges. Therefore, we can say that tetrahedron is also a polyhedron.
Option D.

If we look at the figure in this option, we can make out that it is a solid but it does not have a flat surface. It has a curved surface and is a cone. Thus, it cannot be considered as a polyhedron as it does not satisfy the conditions of a polyhedron.
Therefore, the correct option is option D.

Note: Many students consider a polyhedron as a solid that is joined at their edges only, but we should consider the surfaces too. The surfaces must be flat. Usually students think that only tetrahedron is a polyhedron and end up choosing multiple options as the right answer. But they must note that cube is a regular polyhedron and that prisms are a category of polyhedrons.