Shapes are everywhere in the world. There are various types of shapes in the world, including round, spherical, cylindrical, and more complex shapes.
These shapes have names, and it is good to know them to describe the world around us. We live in a three-dimensional world, where objects have 3-dimensional existence.
You can see that soda cans are cylindrical, while the Earth is spherical. The ice cream base is in the shape of a cone. In this article, we will see in detail what 3D shapes are and how many 3D shapes exist in the world.
What are 3D shapes?
3D is an abbreviation for ‘three-dimensional’, which means solid objects defined by three dimensions. These objects can be measured and described by length, width and depth.
We usually interact with 3D shapes every day. Some common shape names are sphere, cylinder, cone and cube. Even a cuboid, a tetrahedron, and a square-based pyramid are 3D shapes.
Properties of 3D Shapes
3D shapes have three dimensions: length, width, and height. Compared to flat 2D shapes, such as squares or circles, 3D shapes have depth and take up space.
This shape actually exists in the real world. These shaped objects can be found or built everywhere around us, such as boxes, footballs, canned goods, pyramids, etc.
The following are key features of 3D shapes to recognize as 3D objects to help with geometry questions.
- Face: One of the flat surfaces of a solid shape. 3D shapes have various faces. Shapes have faces to define. For example, a cube has six faces.
- Curved Surface: A surface that is rounded, not flat. Some 3D objects have curved faces, such as a sphere that has no faces but a curved surface.
- Vertex: the point at which two or more edges meet. For example, a cuboid has eight vertices, each defining a vertex-wise region.
- Edge: A line segment formed by the intersection of two flat faces or surfaces. For example, a square-based pyramid has eight edges.
Famous 3D shapes every student must know about
Each 3D shape has its own use. In mathematics, you can find shape chapters in every class. Simple parameters for defining 2D shapes are not sufficient for 3D shapes.
These shapes have depth, in addition to width and height, to measure volume. Well-known 3D shapes include cubes, spheres, and cylinders, each with unique properties and uses.
For a 3D structure, you can measure a cube’s surface area and volume. These two terms are major geometric parameters for describing 3D shapes. The area of a shape defines surface area, while volume measures how much space the shape occupies.
Moreover, 3D shapes are broadly classified into polyhedra and non-polyhedra in mathematics. Let's see them in detail.
Polyhedrons
These are 3D shapes entirely made of flat polygonal faces. No curved surface is involved.
Cube
A cube is a common 3D shape that every student should know. It is defined by 6 square faces, 12 edges, and 8 vertices, with all sides equal. Real-life examples include a piece of dice, ice cubes and a gift box pack.
- Area of cube is= Length (l) x width (w)
- Volume of a cube is= Length(l) x Width(w) x Height(h)
Let's say a cube is defined by a length, refer to 'a' here, the volume is equal to length, width and height. The volume of a cube is a3
The surface area of the cube is 6 times the area of a square. 6x a2
Cuboid (Rectangular Prism)
A cuboid shape is a more extended form of a stretched cube, having 6 rectangular faces, 12 edges and 8 vertices. In this shape, all lengths, widths, and heights are different. You can explain this cuboid shape using real-life examples such as books, bricks, and shoeboxes.
- Surface area: 2(lw + lh + wh)
- Volume: length × width × height
Pyramid
This is also a commonly seen shape in the real world. A pyramid is one 3D shape with one flat base and triangular faces meeting at a single point called the apex. There are two types of pyramids: square pyramids and triangular pyramids.
A square pyramid has 1 square base, 4 triangular faces, and the faces meet at a single top point. Another triangular pyramid has 1 triangular base and 3 triangular faces meeting at the top.
The common shape seen is a square pyramid. In real life, you can see Egyptian pyramids, tent tops and decorative roof designs.
- Surface area: base area + area of triangular faces
- Volume: (1/3) × base area × height
Non-Polyhedrons
Non-polyhedral shapes are three-dimensional shapes with curved surfaces, meaning their faces are not flat. These non-polyhedron 3D shapes are defined by their curved surfaces. Common non-polyhedral shapes include spheres, cylinders, and cones.
Consider each shape in detail.
Cylinder
Everyday items, such as cans and pillars, are cylindrical. The cylinder comprises two circular bases attached by a curved plane. An example of this is that can, pipes and batteries are cylindrical in shape.
A cylinder shape would also be an image of a pencil with no pointed ends. A cylinder has two flat circular surfaces and a curved surface.
- Surface area: 2 × pi × r^2 + 2 × pi × r × h
- Volume: pi × r^2 × h
Sphere
A sphere is a perfectly round shape with no edges or vertices. It has only one curved surface. Real-life examples include balls, planets and oranges.
- Surface area of a Sphere = 4Ï€ r2
- Volume a sphere = 4/3(Ï€ r3)
Cone
A cone is a common shape that you have seen in daily life in the form of ice cream cones and traffic cones. A cone has a circular base and a pointed top. It has one circular face, 1 curved face and 1 vertex.
- Surface area: 4 × pi × r^2
- Volume: (4/3) × pi × r^3
How to explain 3D shapes to young students?
For younger students, explaining the properties of 3D shapes can be difficult. To teach them 3D shapes, they need some shapes to play with and create structures or arrangements.
Teachers should explain each 3D shape through charts and shape stacks so students notice small details. The teacher should explain each shape, describing its faces, edges, and vertices.
Students should be exposed to real-world objects to notice common 3D shapes. For example, seeing that an unopened cereal box shape is a cuboid and a ping pong ball shape is a sphere.
Difference between 2D and 3D shape
Students will learn better about three-dimensional objects when they are clear about 2D things. Explain them by clearly drawing a triangle or a square on paper, which is a two-dimensional shape. They don't take up space.
For easy understanding, sketch a circle on a flat page, and tell students it is a 2D object. Now, take an orange from your kitchen and explain that it is a solid that can be perceived as a 3D object.
Assign them an activity to notice 2D shapes in drawings and classroom posters, and 3D shapes in food and other objects. This activity and explanation will easily help students understand 2D and 3D objects.
Common 3D Shapes: Explanation in an Easy Way for Students
Explaining 3D shapes is easy for students when connected with real-life objects. After explaining each object as a lesson, ask them about pointing in daily life. Start teaching them by explaining basic shapes.
Cube
A cube is a 3D shape with 6 square faces of equal size, 12 straight edges, and eight corners. An easy way to remember a cube is that every side is equal and matches. Dice, building blocks, and small gift boxes are the best examples of cubes.
Sphere
Now ask your students to observe the shape of the ball or globe on the table. This shape is called a sphere. There is no plane or flat surface. This type of shape is defined by curved surfaces. A sphere has only one curved surface wrapping all around.
Kids easily understand this shape while playing with a ball. You can also increase their knowledge at this point by telling them that a ball rolls easily due to its spherical shape. Students will also learn the shape, name and fact.
Cylinder
You can teach students about the cylinder shape with soup cans and paper rolls. To explain the shape, tell them about two flat circular faces, one curved surface and two edges.
Explain and repeat the information daily. You can point out tree trunks or bamboo stems as an example beyond the classroom.
Cone
A cone is also a basic shape that exists in this world. Students may notice a cone shape when eating ice cream or seeing coned-shaped traffic markers.
Each cone has one circular base, one curved surface, one edge, and one corner at the tip. For a hands-on experience, let's ask kids to hold a cone-shaped object. This will help them recognize its shape.
Rectangular Prism
A common shape exists in everyday items like shoeboxes and textbooks. You can ask your students to observe the shape and remind them to put their shoes back in the shoe boxes.
A rectangular prism is basically a mix of rectangles and squares. It has six faces, 12 edges and 8 corners. Also highlight to them how a rectangular prism is different from a cube. It is distinct in size and length.
Pyramid
Tell kids about the pyramids of Egypt with images and the structure of shapes. Also, teach them how it differs from a triangle.
A pyramid has one square face at the bottom and four triangular faces meeting at a single point. In the real world, this shape appears on rooftops and in tent designs.
Conclusion
Undoubtedly, the most significant aspect of mathematics and life in general is the 3D shapes. These shapes help us understand the structure and composition of objects in our surroundings.
Starting with cubes, spheres, and cylinders, to pyramids and cuboids, each shape has its own properties to be defined.
These shapes are all around us in the form of buildings, household items and natural objects. A practical and meaningful form of geometry. Learning about 3D shapes sharpens our mathematical skills and problem-solving ability.
The knowledge of 3D shapes develops our skills in mathematics and problem-solving.
The idea of correlating 3D shapes with real-life examples and a practical activity for young kids simplifies understanding and learning.