Nets of 3D Shapes

May 15, 2023

3D shapes are solid shapes or objects that have three dimensions – length, width(or breadth), and height(or thickness), as opposed to two-dimensional objects which have only a length and a width(or breadth). They have depth and so they occupy some volume.

Nets of 3D shapes are the basic skeleton outline in two dimensions, which can be folded and glued together to obtain the 3D structure. Let’s understand the process of making 3D shapes using nets with the help of 2D shapes.

Nets of 3D shapes are 2D shapes that can be folded to form 3D shapes or solids. A net can be defined as a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets. A net can be viewed as a flattened-out three-dimensional solid. It is the basic skeleton outline in two dimensions, which can be folded and glued together to obtain the 3D structure.

Let’s understand the nets of the following 3D shapes.

Cuboid
Cube
Cylinder
Cone
Prism
Pyramid

Net of a Cuboid

A cuboid has six faces. Each face of the cuboid is a rectangle. Therefore, when a cuboid is unfolded it will give $6$ rectangles. Thus to draw a net of a cuboid, we need to draw $6$ rectangles connected to each other in a particular sequence.

There are $54$ different nets of the cuboid. A few nets of the cuboid are shown below.

Net of a Cube

A cube has six faces. Each face of the cube is a square. Therefore, when a cube is unfolded it will give $6$ squares. Thus to draw a net of a cube, we need to draw $6$ squares connected to each other in a particular sequence.

There are $11$ different nets of the cuboid. A few nets of the cuboid are shown below.

Net of a Cylinder

A cylinder has three faces. Two of these faces are circular and one is rectangular. Therefore, when a cube is unfolded it will give $2$ circles and $1$ rectangle. Thus to draw a net of a cylinder, we need to draw $2$ circles and $1$ rectangle connected to each other in a particular sequence.

Net of a Cone

A cone has two faces. One face is curved and the other one is flat. Therefore a net of cones has two parts – one is the circle which represents the flat part and the second one is the sector which represents the curved part. Thus to draw a net of a cone, we need to draw $2$ polygons one sector of a circle and another a full circle.

Net of a Prism

A prism is a three-dimensional solid that has identical polygonal bases at both ends. The other faces are parallelograms or rectangles. The number of rectangular or parallelogram faces is equal to the number of sides of polygonal bases. A prism is named after its base such as a triangular prism, pentagonal prism, and hexagonal prism.

Net of a Triangular Prism

A triangular prism has two triangular bases and three rectangular faces. Therefore, when a triangular prism is unfolded it will give $5$ polygons – $2$ triangles and $3$ rectangles. Thus to draw a net of a triangular prism, we need to draw these $5$ polygons connected to each other in a particular sequence.

Net of a Pentagonal Prism

A pentagonal prism has two pentagonal bases and five rectangular faces. Therefore, when a pentagonal prism is unfolded it will give $7$ polygons – $2$ pentagons and $5$ rectangles. Thus to draw a net of a pentagonal prism, we need to draw these $7$ polygons connected to each other in a particular sequence.

Net of a Hexagonal Prism

A hexagonal prism has two hexagonal bases and six rectangular faces. Therefore, when a hexagonal prism is unfolded it will give $8$ polygons – $2$ hexagons and $6$ rectangles. Thus to draw a net of a hexagonal prism, we need to draw these $8$ polygons connected to each other in a particular sequence.

Net of a Pyramid

A pyramid is a 3D figure constructed with a polygonal base and triangular faces all connected together. A pyramid connects each vertex of the base to a common tip or apex giving it the typical shape. The number of triangular faces is equal to the number of sides of the polygonal base. A prism is named after its base such as a triangular pyramid, square pyramid, pentagonal pyramid, and hexagonal pyramid.

Net of a Triangular Pyramid

A triangular pyramid has one triangular base and three triangular faces. Therefore, when a triangular pyramid is unfolded it will give $4$ triangles. Thus to draw a net of a triangular pyramid we need to draw these $4$ triangles connected to each other in a particular sequence.

Net of a Square Pyramid

A square pyramid has one square base and four triangular faces. Therefore, when a square pyramid is unfolded it will give $1$ square and $4$ triangles. Thus to draw a net of a square pyramid we need to draw these $5$ polygons connected to each other in a particular sequence.

Net of a Pentagonal Pyramid

A pentagonal pyramid has one pentagonal base and five triangular faces. Therefore, when a pentagonal pyramid is unfolded it will give $1$ pentagon and $5$ triangles. Thus to draw a net of a pentagonal pyramid we need to draw these $6$ polygons connected to each other in a particular sequence.

Examples on Nets of 3D Shapes

Example 1: Identify the nets which can be used to form cubes.

Nets for a cube are (ii), (iii), and (iv)

Example 2: The edge of a cuboid is 4 cm, 5 cm, 10 cm. Draw a net of the cuboid. What will be the surface area of a cuboid?

Surface Area of cuboid = Area of $1$ + Area of $2$ + Area of $3$ + Area of $4$ + Area of $5$ + Area of $6$.

Area of $1$ = $10 \times 4 = 40 \text{ cm}^2$

Area of $2$ = $5 \times 4 = 20 \text{ cm}^2$

Area of $3$ = $10 \times 5 = 50 \text{ cm}^2$

Area of $4$ = $5 \times 4 = 20 \text{ cm}^2$

Area of $5$ = $10 \times 4 = 40 \text{ cm}^2$

Area of $6$ = $10 \times 5 = 50 \text{ cm}^2$

Total surface area of cuboid = $40 + 20 + 50 + 20 + 40 + 50 = 220 \text{ cm}^2$

Example 3: Identify the 3D shape from the following net.

The above net has two triangles and three rectangles, therefore it is a net of a triangular prism, with two triangular bases and three rectangular faces.

Practice Problems

Draw the net of the following 3D shapes

a cuboid with dimensions $9$ cm, $5$ cm, and $4$ cm
a cube of edge $5$ cm
a cylinder of base radius $2$ cm and height $6$ cm
a cone of base radius $3$ cm and height $4$ cm
a triangular prism with a side of a triangular base of $3$ cm and a height of $4$ cm
a triangular pyramid with a side of a triangular base of $3$ cm and a height of $4$ cm

FAQs

What is meant by a net of 3D shapes?

A net can be defined as a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

How many different nets of a cuboid are possible?

There are $54$ different nets of the cuboid.

How many different nets of a cube are possible?

There are $11$ different nets of the cube.

How many triangles are required to make a net of a triangular prism?

Since a triangular prism has two triangular bases and three rectangular faces, therefore two triangles are required to make a net of a triangular prism.

How many triangles are required to make a net of a triangular pyramid?

Since a triangular pyramid has one triangular base and three triangular faces, therefore four triangles are required to make a net of a triangular pyramid.

Conclusion

Nets of 3D shapes are 2-D shapes that can be folded to form 3D shapes or solids. Nets of 3D shapes are the basic skeleton outline in two dimensions, which can be folded and glued together to obtain the 3D structure.

Nets of 3D Shapes – Meaning, Types & Examples