Definition properties formulas and examples of three dimensional shapes
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.
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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.
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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.
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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
Square prism
Triangular prism
Pentagonal prism
Hexagonal prism
3. Platonic Solids or Polyhedrons
There are only five platonic solids:-
Tetrahedron: it is made up of 4 equilateral triangular faces.
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Octahedron: It is made up of 8 equilateral triangular faces.
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Cube: It is made up of 6 square shaped faces.
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Dodecahedron: It is made of pentagons. Also it has 12 sides.
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Icosahedron: It is made of triangles. Also it has 20 sides.
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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.
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Now let us dive deeper into faces, edges and vertices of basic 3d shapes.
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Did you know?
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.
Scientists believe that there are more than four dimensions in space.
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.
FAQs on Understanding 3 Dimensional Shapes in Geometry
1. What are 3 dimensional shapes in maths?
3 dimensional shapes are solid figures that have length, width, and height and occupy space. Unlike 2D shapes, they have volume and thickness.
- They are also called 3D shapes or solid shapes.
- They have faces (flat surfaces), edges (line segments), and vertices (corners).
- Examples include cube, cuboid, sphere, cylinder, cone, and pyramid.
2. What are the examples of common 3D shapes?
Common 3D shapes include cube, cuboid, sphere, cylinder, cone, and pyramid. These shapes are frequently used in geometry problems and real life.
- Cube: All faces are squares.
- Cuboid: Rectangular box shape.
- Sphere: Perfectly round like a ball.
- Cylinder: Two circular bases and one curved surface.
- Cone: One circular base and a vertex.
- Pyramid: A polygon base with triangular faces meeting at a point.
3. What is the difference between 2D and 3D shapes?
The main difference is that 2D shapes have length and width, while 3D shapes have length, width, and height. This means 3D shapes occupy space and have volume.
- 2D shapes: Square, rectangle, triangle, circle.
- 3D shapes: Cube, sphere, cylinder, cone.
- 2D shapes have area only, but 3D shapes have volume and surface area.
4. What is the formula for the volume of a cube?
The volume of a cube is given by V = a³, where a is the length of one side. Since all edges of a cube are equal, the volume is found by multiplying the side by itself three times.
- Example: If side = 4 cm
- V = 4 × 4 × 4 = 64 cm³
5. How do you find the surface area of a cuboid?
The surface area of a cuboid is calculated using 2(lb + bh + hl), where l = length, b = breadth, and h = height. This formula adds the areas of all six rectangular faces.
- Example: l = 5 cm, b = 3 cm, h = 2 cm
- Surface area = 2(15 + 6 + 10)
- = 2 × 31 = 62 cm²
6. What is the volume formula for a cylinder?
The volume of a cylinder is given by V = πr²h, where r is the radius of the base and h is the height. It represents the area of the circular base multiplied by the height.
- Example: r = 3 cm, h = 5 cm
- V = π × 9 × 5 = 45π ≈ 141.37 cm³
7. How many faces, edges, and vertices does a cube have?
A cube has 6 faces, 12 edges, and 8 vertices. Each face is a square and all edges are equal in length.
- Faces: 6 square faces
- Edges: 12 equal edges
- Vertices: 8 corners
8. What is the formula for the volume of a cone?
The volume of a cone is calculated using V = (1/3)πr²h, where r is the radius and h is the height. It is one-third the volume of a cylinder with the same base and height.
- Example: r = 3 cm, h = 6 cm
- V = (1/3) × π × 9 × 6
- = 18π ≈ 56.55 cm³
9. What is the surface area of a sphere?
The surface area of a sphere is given by 4πr², where r is the radius. This formula measures the total outer curved surface of the sphere.
- Example: r = 7 cm
- Surface area = 4π × 49
- = 196π ≈ 615.75 cm²
10. What are the properties of 3D shapes?
The main properties of 3D shapes include having faces, edges, vertices, surface area, and volume. These properties describe how solid shapes are structured and measured.
- Faces: Flat or curved surfaces.
- Edges: Line segments where faces meet.
- Vertices: Points where edges meet.
- Surface area: Total area of all faces.
- Volume: Space occupied by the solid.
