[Maths Class Notes] on 3 Dimensional Shapes Pdf for Exam

Have you ever thought about why distance between two objects is considered to be the minimum distance? Why the distance between two points on the number line is just the difference of those two points. Why “area” is 2d phenomena. In this section we are going to focus on answers to all these questions. First of all we’ll try to understand what dimension is. Then we’ll learn basic 3 dimensional objects or shapes with their properties.

Definition of Dimension:

Dimension is nothing but direction in which we are going to measure an object or shape into per unit measurement. 

When we say 1D, it means we are dealing in a single direction only. In mathematics, it is a number line on which we represent all numbers from left to right direction. 2D means we are talking about 2 dimensions or directions. In mathematics, it is coordinate geometry. There we have 2 directions which are x axis and y axis. These are mutually perpendicular to each other. Any shape on a plane surface is called 2D shape. For example: rectangle. 

In the similar fashion, 3D means three dimensional or directional shapes or objects. When we try to measure any object in 3 directions then we say an object is 3D or 3 dimensional. In mathematics there is a topic with the same name. There the dimensions used to be x axis, y axis and z axis. There three are mutually perpendicular to each other. The attribute of three dimensional objects are face, edge and vertices.

3 Dimensional Shapes

The common examples of 3D objects are cube, cuboid, rectangular prism, sphere, cone and cylinder.

We live in a 3 dimensional space. Here a lot of things resemble the common 3 dimensional objects. For example a football or a basketball is nothing but a sphere. A rubik’s cube or a die is the shape of a cube. A pencil box and rubber is of rectangular prism shape. Poll and water bottles have cylindrical shape.

More 3D Shapes

Since, we know the basic 3D shapes. Let’s discuss some more 3 Dimensional shapes and their properties.

1. Pyramid: 

A pyramid is also a three-dimensional (3D) shape. It has a polygon base and flat (triangular) sides that join at a point which is called the apex. 

2. Prism: 

A prism is a form of three-dimensional (3D) shape with flat sides. It has two ends that are of equivalent shape and size (and appear as if a 2D shape). It has an equivalent cross-section right along the form from end to end; meaning if you narrow through it you’d see an equivalent 2D shape as on either end. There are many different types of prism. Some of them are

1. Square prism

2. Triangular prism

3. Pentagonal prism

4. Hexagonal prism

3. Platonic Solids or Polyhedrons

There are only five platonic solids:-

1. Tetrahedron: it is made up of 4 equilateral triangular faces.

2. Octahedron: It is made up of 8 equilateral triangular faces.

3. Cube: It is made up of 6 square shaped faces.

4. Dodecahedron: It is made of pentagons. Also it has 12 sides.

5. Icosahedron: It is made of triangles. Also it has 20 sides.

About 3d Shapes

We discussed that, for all 3 dimensional shapes we commonly talk about three attributes. Which are face, edge and vertices. First of all let us define what they are and then we’ll discuss attributes of 3 Dimensional shapes.

Face: Faces are flat surfaces in 3 dimensional shapes.

Vertices: Vertices are the points where 3 faces meet.

Edge: Edges are the lines where 2 faces meet.

Now let us dive deeper into faces, edges and vertices of basic 3d shapes.

Did you know?

1. In modern science, scientists have developed a fourth dimension also, which is time. Anything in our world in which it is necessary to consider time constraints, is in the fourth dimension. For example: If we chop a fruit and let it be for one day then after a day it would not be the same as it was before. It’ll be rotten. This whole phenomenon is in the fourth dimension. Another example is taking a train or flight. With the location of a railway station or airport (which is in 3 dimensions) we need to specify the time also, so that the person can be at that place at a particular time. This scenario is also considered in the fourth dimension.

2. Scientists believe that there are more than four dimensions in space.

3. In maths there is a subject with the name linear algebra. In this we talk about n dimensional space but the problem is, it’s not the same as what we think of it. It is just using the name “dimension” other than this, it has its own definition of dimension and vector space.