What Are the Main Differences Between 2D and 3D Shapes?
Geometry is a study of shapes. It is broadly classified into two types: plane geometry called 2d shapes and solid geometry called 3d shapes. Let us draw a picture of a notebook on a piece of paper. What we observe is a plain picture drawn on paper. It does not occupy any space called 2d shapes, but if we keep a real notebook on that piece of paper it occupies some space, and such shapes are called 3d shapes or three-dimensional shapes.
Plane geometry or two-dimensional geometry deal with the flat figures that can be drawn on a piece of paper like line, curves, polygons, quadrilaterals, etc, while solid geometry or three-dimensional geometry deals with solid shapes or three-dimensional shapes. Examples of three-dimensional shapes are sphere, cylinders, cones, etc.
What are 2D Shapes?
In geometry, a shape or a figure that has two dimensions namely a length and a breadth is called a 2D shape. In other words, a plane object that has only length and breadth is a 2 dimensional shape. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides.
There are no fixed properties of the 2D shape. As each shape has a different number of sides and for each shape, properties vary. But, every 2D shape is flat and is enclosed.
Definition of 2D Shapes
In geometry, 2D shapes can be defined as completely flat plane figures and only two dimensions - length and width. They are not thick and can only be measured in two dimensions. A polygon is a 2-Dimensional shape composed of vertical line segments connected to one another, thus giving it a closed shape. Circles, squares, rectangles, and triangles are some examples of two-dimensional objects and these shapes can be drawn on paper. Except for the circle which is a curved figure, all 2-D shapes have sides, corners, and internal angles. 2D Figures have at least three 2D straight sides and they are known as polygons and that includes triangles, squares, and quadrilaterals.
What are 3D Shapes?
The shapes that occupy space are called 3D shapes. 3D shapes can also be defined as the solid shapes having three dimensions length, width, and height. A football is an example of the sphere which is a three-dimensional figure while a circle drawn on a piece of paper is a two- dimensional figure. Similarly, we have many 3D shapes all around us like a table, chair, notebook, pen, etc.
Definition of 3D Shapes
3D shapes are solid objects or objects with three dimensions (length, width, and height), compared to objects with only two sides in length and width. The most important terms with the geometric shapes of 3D are faces, edges, and vertices. They have a depth so they take a certain amount of volume. Some 3D shapes have their base and top parts or cross sections such as 2D shapes. For instance, The cube has all the square-shaped sides. Now we will learn more about each 3D shape. 3D environments are divided into several categories. Some of them have curved areas; others are in the form of pyramids or prisms.
Terms Used For 3D Figures
Face. The face is a flat or curved area in 3D shape. For example a cube has six faces, a cylinder has three faces and a circle has one face.
Edges. Edge is the corner where two points meet .
Vertices. The vertex is where the edges meet.
Difference Between 2D and 3D Shapes: Tabular Form
Solved Examples:
Example 1:
Find the volume and surface area of a cuboid of l= 10cm, b = 8cm and h = 6 cm.
Solution:
We have Volume of cuboid = V = l x b x h
= 10 x 8 x 6
= 480cm2
Surface area = 2 ( lb + lh + bh)
= 2( 10x8 + 10x6 + 8x6)
= 2(80 + 60 + 48)
= 376cm2
Example 2:
The length of the rectangular field is 15m and width is 6m. Find the area and perimeter of the field.
Solution:
Given that Length = 15m
Width = 6m
We have, Area formula A = length x width
= 15 x 6
= 90 m2
And Perimeter formula P = 2 (length + width)
= 2 x (15 + 6)
= 2 x 21
= 42 m.
Quiz Time
1.Find the area of the right-angled triangle whose base is 12cm and hypotenuse 13cm.
40 cm
85 cm
60 cm
30cm2
2. The side of a square whose surface area is 600cm is
10cm
20 cm
30 cm
40 cm
Fun Facts
3D graphics are used in computers to make video games or animated movies.
Some people consider time as a fourth dimension.
FAQs on 2D and 3D Figures: Definitions, Properties, and Examples
1. What is a 2D shape in mathematics?
A 2D (two-dimensional) shape is a flat figure that has only two dimensions: length and width. It does not have any thickness or depth, which means it can be drawn on a piece of paper but cannot be held physically. Common examples include circles, squares, rectangles, and triangles.
2. What defines a 3D shape and makes it different from a 2D shape?
A 3D (three-dimensional) shape is a solid object that has three dimensions: length, width, and height (or depth). Unlike a 2D shape, a 3D shape occupies space. The key difference is the third dimension, which gives it volume. For instance, a square is a 2D shape, but a cube, which is made of square faces, is a 3D shape.
3. What are the main properties used to describe 2D shapes?
The main properties of 2D shapes, especially polygons, are their sides and vertices (corners).
- Sides: These are the straight line segments that form the boundary of the shape. A triangle has 3 sides, and a square has 4.
- Vertices: This is the point where two sides meet. A triangle has 3 vertices, and a square has 4.
For a shape like a circle, the key property is its radius or diameter.
4. What are faces, edges, and vertices in a 3D shape?
The properties of most 3D shapes (polyhedrons) are described using faces, edges, and vertices:
- Faces: These are the flat surfaces of the 3D shape. For example, a cube has 6 square faces.
- Edges: An edge is a line segment where two faces meet. A cube has 12 edges.
- Vertices: A vertex is a corner point where multiple edges and faces meet. A cube has 8 vertices.
5. Can you give some examples of 2D and 3D shapes we see in everyday life?
Yes, we are surrounded by 2D and 3D shapes.
- Examples of 2D Shapes: The face of a clock (circle), a single page of a book (rectangle), a slice of pizza (triangle), and a chessboard square (square).
- Examples of 3D Shapes: A football (sphere), a dice (cube), a party hat (cone), and a can of soda (cylinder).
6. How can a 2D shape be used to form a 3D shape?
Many 3D shapes are formed from 2D shapes. For example, a cuboid is a 3D shape that is formed using six 2D rectangular faces. Similarly, a cylinder can be thought of as being formed by two 2D circular bases and a rolled-up rectangular surface. This shows that 2D figures are the fundamental building blocks for many 3D objects.
7. Why is it important to understand the difference between 2D and 3D figures in Maths?
Understanding the difference is crucial for progressing in geometry and real-world applications. For 2D shapes, we focus on calculating properties like area and perimeter. For 3D shapes, we move on to more complex concepts like volume and surface area. This knowledge is essential in fields like architecture, engineering, and design, where professionals work with spatial plans (2D) to construct real objects (3D).
8. Can a 3D shape exist without any flat faces or straight edges?
Yes, a 3D shape can be composed entirely of a curved surface. The most common example is a sphere (like a ball). It has no flat faces, no edges, and no vertices. It is a perfectly round three-dimensional object where every point on its surface is equidistant from its centre. This makes it different from polyhedrons like cubes or pyramids.
