News & Events
Understanding 3D Shapes: Faces, Edges, and Vertices
Geometry is a part of mathematics that contains different shapes and sizes. It is divided into two types- Plane and solid geometry. Plane geometry works with flat shapes such as polygons, lines, curves, etc. While three-dimensional geometry deals with three-dimensional shapes (3D) such as cubes, cylinders, spheres and cuboids. As the name suggests, three-dimensional shapes are measured in three dimensions- Length, breadth and width. On the other hand, two-dimensional shapes have two dimensions- length and width. In this article, we will help you learn about 3D shapes by explaining different types of 3D shapes, their attributes and more.
What are the different attributes of 3d shapes?
Face, edges and vertices are three attributes of three-dimensional shapes. The face is the flat surface of a shape, the edge is the line segment where two faces meet and vertices is the point where three edges meet.
Types of 3D shapes
Several three-dimensional shapes exist each with different volume, surface area and bases. Let us discuss them in detail.
1. Sphere
The sphere is a three-dimensional shape that is round in shape and all points on its surface are equidistant from the centre. Our earth looks like a sphere but it is not. It is a spheroid whose radius from the centre to the surface is not the same at all points. Some other characteristics of the sphere are as follows.
- It is perfectly symmetrical.
- It has radius, circumference, volume and surface area.
- A sphere has no vertex, no edges and one curved face.
2. Cube and cuboid
Cube and cuboid have the same Vertices, edges and faces. The major difference between a cube and a cuboid is that all six faces of the cube are squares and all the six faces of the cuboid are rectangles. The length, width and height of a cube are the same but the length, width and height of a cuboid are not the same.
3. Cylinder
A cylinder contains two circular/elliptical faces one at the top and the other at the bottom. These two circular faces/bases are connected by a curved surface. The distance between two bases is the height “h” and the distance from the outer surface to the axis is the radius “r”. Some properties of a cylinder are as follows.
- It has one curved surface and two identical flat (circular or elliptical) faces.
- A cylinder does not have a vertex like a cube or cuboid.
- The top and bottom faces of the cylinder are identical.
4. Cone
A cone is a three-dimensional space that has a pointed tip and a flat base. Its pointed tip is called apex and its base is a circle/oval. The cone is found in various objects such as Ice cream cones and traffic cones.
Some properties of a cone are as follows
- A cone is called a right-angle cone when its apex is perpendicular to the base. On the other, a cone is called an oblique cone, if the apex is not perpendicular to the centre of the base.
- A cone has a height and radius just like a cylinder. But it also has slant height which is the distance between the apex and any point on the circumference.
5. Pyramid
A pyramid is a polygon whose outer surfaces are triangles which meet at a single top. Its base can be of any shape- Triangular, square or quadrilateral. The most common pyramid is a square pyramid which has four triangular faces and one square base. Some other types of pyramids are-
- Square pyramids
- Triangular pyramids
- Hexagonal pyramids
- Pentagonal pyramids
6. Prism
Prisms are three-dimensional shapes with flat surfaces or faces and identical polygon ends. Here are some characteristics of the prism.
- It is classified into regular and oblique prisms.
- Some common types of prisms are triangular prisms, square prisms, hexagonal prisms and more.
- It does not have any curve.
Faces, edges and vertices of 3D shapes
Here are the faces, edges and vertices of different 3D shapes. You will learn about these attributes in detail while studying in top CBSE schools in Baddi. Incorporating the knowledge that we have given here with your school's teaching on 3D shapes will enhance your overall learning experience.
| 3-D Shape | Vertices | Faces | Edges |
| Sphere | 0 | 1 | 0 |
| Cube | 8 | 6 | 12 |
| Cuboid | 8 | 6 | 12 |
| Cylinder | 0 | 3 | 2 |
| Cone | 1 | 2 | 1 |
| Square Pyramid | 5 | 5 | 8 |
| Triangular Pyramid | 4 | 4 | 6 |
| Pentagonal Pyramid | 6 | 6 | 10 |
| Hexagonal Pyramid | 7 | 7 | 12 |
| Rectangular Pyramid | 8 | 6 | 12 |
| Triangular Prism | 6 | 5 | 9 |
| Pentagonal Prism | 10 | 7 | 15 |
| Hexagonal Prism | 12 | 8 | 18 |
Surface area and volume of three-dimensional shapes
3-D shapes have surface area and volume, and every shape has its specific formulas to calculate both. Surface area is the area at the bottom, top faces and other curved surfaces of a 3D shape. On the other hand, the space occupied by a solid shape is referred to as volume. Here are the surface area and volume of different 3-D dimensional shapes.
| Solid Shape | Formulas |
| Sphere | Surface area= 4πr2, Volume= (4/3)πr3 |
| Cube | Surface area= 4a2, Volume= a3 |
| Cuboid | Lateral Surface area= 2h(l + w), Volume= (l × w × h) |
| Cylinder | Total surface area= 2πr(h+r), Volume= πr2h |
| Cone | Surface area= πrl, Volume= (1/3)πr2h |
| Pyramid | Surface area= Base Area + (1/2 × Perimeter × Slant Height), Volume= [(1/3) × Base Area × Altitude] |
| Prism | Surface area=[(2 × Base Area) + (Perimeter × Height)], Volume= (Base Area × Height) |
Why is it important for children to learn about three-dimensional shapes?
Three-dimensional shapes help children understand how objects exist in space, which helps in developing their spatial abilities. Moreover, many objects in the real world are three-dimensional, so teaching children about 3D shapes helps them recognise and contemplate everyday objects such as cubes and spheres. The best schools in Nalagarh introduce children to 3D concepts such as surface area and volume. Understanding these fundamental concepts helps them in advanced mathematical studies.
The key takeaways
We are surrounded by three-dimensional objects, from household items, vehicles, and everyday objects to buildings and structures. Understanding these will not only help children in the examination but also aid in analyzing the designs of things. Also, many disciplines in higher education rely on the principle of three-dimensional objects, which makes it even more important to understand them deeply.
