Nets for Building 3D Shapes: Figues which have only length are known as one-dimensional figures. A line is a one-dimensional figure. Figures having length and breadth are known as two-dimensional figures. A polygon, a circle etc., are two-dimensional figures. Objects and shapes having length, breadth and height are known as three-dimensional objects and shapes. Three-dimensional shapes are known as \(3D\) shapes.

In this article, we will learn to draw a net for some three-dimensional shapes. A net is a three-dimensional solid that has been flattened. It’s a two-dimensional skeleton outline that can be folded and bonded together to become a three-dimensional construction. Nets are used to create three-dimensional shapes.

Three-Dimensional Shapes

In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us, which have different shapes. One thing common about most of these objects is that they all have some length, breadth, height, or depth. That is, they all occupy space and have three dimensions. Hence, they are called three-dimensional shapes. 

The sole distinction between \(2D\) and \(3D\) shapes is that \(2D\) shapes lack thickness and depth. In most cases, \(3D\) objects are created by rotating \(2D\) shapes. The \(2D\) shapes are the faces of solid shapes.

A cube, cuboid, cone, cylinder, sphere, prism, etc., are \(3D\) shapes. Both curved shaped solids and the straight-sided polygon faced solids known as the polyhedrons make up the \(3D\) forms. Polyhedrons, which are built on \(2D\) structures with straight sides, are also known as polyhedra. Let’s go into the specifics of polyhedrons and curved solids now.

Different solid shapes are classed based on three essential criteria. The three key characteristics that distinguish \(3D\) shapes are listed below:

(i) Faces: Polygons forming a polyhedron are known as faces.

(ii) Edges: Line segments common to intersecting faces of a polyhedron are known as its edges.

(iii) Vertices: Points of intersection of edges of a polyhedron are known as its vertices. In a polyhedron-three or more edges meet at a point to form a vertex.

Polyhedrons

The word polyhedra are the plural of a polyhedron which may be defined as a solid shape bounded by polygons. Like a polygon, we have different polyhedron types as regular, irregular, concave and convex polyhedrons.

The regular polyhedrons with identical faces are also known as platonic solids. Two important members of the polyhedron family are prisms and pyramids. So, let us know about these two polyhedrons.

Prism

A prism is a solid whose side faces are parallelograms whose ends (or bases) are congruent parallel rectilinear figures.

In the above figure, there is a prism whose ends are rectilinear figures \(ABCDE\) and \(A’B’C’D’E’\)

Pyramid

A pyramid is a polyhedron whose base is a polygon of any number of sides and whose other faces are triangles with a common vertex. Below is an example of a pentagonal pyramid.

Curved Solids

Aside from polyhedrons, there are curved \(3D\) shapes such as the sphere, cone, and cylinder. Cones, for example, have a round base that narrows gradually from the circular base to the apex. Because all of these shapes have curved faces, they are referred to as curved solids.

Nets for Building 3D Shapes

To understand three-dimensional objects more closely, we try to form these objects from their nets. A net for a three-dimensional shape is nothing but a skeleton outline in \(2\)-dimension which, when folded, results in three-dimensional shapes. To understand this, let us perform the following activity: 

Take a cardboard box. Cut the edges to lay the box flat. You have now a net for that box. A net is a skeleton outline in \(2D\) as shown in the first figure, which, when folded as shown in the second figure, results in a \(3D\) shape as shown in the third figure.

By adequately separating the edges, you were able to create a net. Is it possible to reverse the process?

Here is a net pattern for a box in the below figure. Copy and enlarge the net version and try to make the box by suitably folding and glueing together. (You may use suitable units). The box is solid. It is a \(3D\) object with the shape of a cuboid.

Thus, we can say that a net for a three-dimensional shape is a two-dimensional shape that can be cut out of a piece of paper or cardboard such that by folding it, the three-dimensional shape can be formed.

Net Pattern for a Cube

A cube is a three-dimensional object with six square faces that are all the same size and exact dimensions. A cube has \(6\) faces, \(12\) edges and \(8\) vertices. The net for a solid cube is shown below.

We can draw \(11\) nets for a cube.

Net Pattern for a Cuboid

A three-dimensional solid shape with \(6\) rectangular faces, \(8\) vertices, and \(12\) edges is known as a cuboid. It is one of the most commonly seen shapes around us.

Net for a solid cuboid is shown below.

We can draw \(54\) nets for a cuboid.

Net Pattern for a Cylinder

A cylinder is a solid three-dimensional form made up of two parallel bases connected by a curved surface. These bases are shaped like a round disc. The cylinder’s axis is a line that runs from the centre or connects the centres of two circular bases. The height represents the distance between the two bases of the cylinder, which is termed perpendicular distance.

A cylinder has \(3\) faces, \(2\) edges and \(0\) vertices.

Net for a solid cylinder is shown below.

Net Pattern for a Cone

A three-dimensional shape with a circular base narrows down to a sharp point called a vertex is called a cone.

A cone has one vertex, one curved edge, one curved face and one flat face. The net for a solid cone is shown below.

Net Pattern for a Triangular Prism

A three-dimensional shape with two identical ends in the shape of a triangle connected by similar parallel lines is known as a triangular prism. It’s a polyhedron with three rectangular sides and two parallel and congruent triangle bases on each side.

The net for a triangular prism is shown below

Net Pattern for a Square Pyramid

A square pyramid is a three-dimensional geometric form with a square base and four triangular faces/sides that meet at a single point. This pyramid is an equilateral square pyramid if all of the triangular faces have equal edges.

A square pyramid has \(5\) faces, \(5\) vertices and \(8\) edges.

The net for a square pyramid is shown below

Net Pattern for a Hexagonal Pyramid

A hexagonal pyramid is a three-dimensional pyramid with a hexagonal base and sides or faces in the shape of isosceles triangles.

The net for a hexagonal pyramid is shown below.

Net Pattern for a Tetrahedron

A polyhedron with \(4\) faces, \(6\) edges and \(4\) vertices, and triangular faces is known as a tetrahedron.

The nets for a tetrahedron is shown below

Solved Examples on Nets for Building 3D Shapes

Q.1. Identify the nets which can be used to make cubes.

Ans: The cube has six squared faces. So the nets that are used to make cubes are:
(ii), (iv) and (vi)

Q.2. Can the following be a net for a die? Explain your answer.

Ans: The given net of a die can be folded as shown below.

Here, we can observe that when the given net is folded, the opposite faces of the die-formed have \(2\) and \(5, 1\) and \(4, 3\) and \(6\). If we add those, we get \(7, 5, 9,\) respectively. But, in a die, the total of the numbers on the opposite faces must be equal to \(7.\) Therefore, the given net cannot form a die.

Q.3. Out of the following four nets, there are two correct nets to make a tetrahedron. Identify them.

Ans: From the given nets, the nets that can be tetrahedrons are (i) and (iii).

Q.4. Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there on the net here? (Give two separate diagrams.) 

Ans: In the given net, we have \(3\) faces. We can complete the given net for making a cube as follows. 

Q.5. Write the name of a polyhedron using the below net.

Ans: The given net consists of two triangular faces and three rectangular faces. So, the given net is a triangular prism.

Summary

In this article, we have studied the meaning of three-dimensional shapes, the definition of the polyhedron and curved solids. 3D shapes involve a cube, cuboid, cone, cylinder, sphere, prism, etc. Furthermore, curved shaped solids and straight-sided polygon faced solids which are also referred to as polyhedrons make up the 3D forms.

In this article, we learned that a net for a 3D shape is a 2D shape that is cut on a piece of paper such that the 3D shape can be formed. Also, we have learned the definition of nets of three-dimensional solid and how to draw a net for a cube, cuboid, cylinder, cone, triangular prism, square pyramid and hexagonal pyramid and tetrahedron. Also, we solved some example problems based on nets for building three-dimensional shapes.

Learn About Different Geometrical Shapes

FAQs on Nets for Building 3D Shapes

Q.1. What are the nets of 3D shapes?
Ans: A net for a three-dimensional shape is a two-dimensional shape that can be cut out of a piece of paper or cardboard such that by folding it, the three-dimensional shape can be formed.

Q.2. How many nets can be drawn for a cube?
Ans: We can draw \(11\) nets for a cube.

Q.3. Which 3D shape can be made from a 2D net?
Ans: Some examples of \(3D\) shapes are a cube, cuboid, cone, cylinder, prism, etc. The polyhedrons are based on \(2D\) shapes with straight sides. So, we can make all polyhedrons and curved solids in \(3D\) shape using a \(2D\) net.

Q.4. How are nets useful in real life?
Ans: To find the area of the given solid, we can use the \(2D\) nets.

Q.5. Can a solid have different nets?
Ans: Yes, a solid can have different nets.
Example: A cube has \(11\) nets, whereas a cuboid has \(54\) nets.

We hope this detailed article on nets for building 3D shapes helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!