Geometry - Dimensions

• What is Dimension?
• Types of Shapes Based on Dimensions
• Solved Examples
• Practice Problems
• Frequently Asked Questions

What is Dimension?

Dimension is the measurement of size or distance in the form of length, width, and height of an object, a region, or anything that exists in space. Some common ways to express dimensions are:

• Length 
• Width
• Height

Types of Shapes based on Dimensions

There are several shapes that can be classified into different categories based on dimensions. Some of them are: 

`1`. Zero-dimensional shape: A zero-dimensional shape is used to indicate the location only. There is no length, width, or height in a zero-dimensional shape. It is just a point.

• 

(A zero-dimensional shape)

`2`. One-dimensional shape: A one-dimensional shape has only length. A line segment is a one-dimensional shape.

___________________________________________  

(A one-dimensional shape)

`3`. Two-dimensional shape: A two-dimensional shape has only two dimensions length and width. Squares, rectangles, and circles are some of the examples of two-dimensional shapes.

(Some two-dimensional shapes)
 

A two-dimensional shape can be referred using two axes `x` and `y`.

`4`. Three-dimensional shape: A three-dimensional shape has three dimensions: length, width, and height. A rectangular prism is an example of three-dimensional shape.

(A rectangular prism) 

A three-dimensional shape can be referred using three axes `x, y,` and `z`.

Solved Examples

Example `1`: In how many dimensions can we measure the object shown below?

Solution: 

The object shown is a glass of water. The glass has length, width, and height. So, it is a three-dimensional object.

Example `2`: How many dimensions does a point have? 

Solution:

A point has no dimension. So, it has zero dimensions.

Example `3`: Find the dimensions of the shape shown below:

 Solution: 

The given shape is a circle. It has two dimensions, length and width, which are the same and we call them diameter.

Practice Problems

Q`1`. Which of the following objects has two dimensions?

1. Sphere
2. Cylinder
3. Triangle
4. Cube

Answer: c

Q`2`. In geometry, which of the following is an example of a one-dimensional object?

1. Square
2. Line segment
3. Triangle
4. Circle

Answer: b

Q`3`. Among the given options, which represents a real-life three-dimensional object?

1. Mirror
2. Basketball
3. Bookmark
4. String

Answer: b

Q`4`. What is the dimensionality of an aquarium?

1. `0` Dimension
2. `1` Dimension
3. `2` Dimensions
4. `3` Dimensions

Answer: d

Q`5`. Which of the following mathematical concepts is considered to have no dimensions?

1. Point
2. Line
3. Circle
4. Square

Answer: a

Frequently Asked Questions

Q`1`. How many dimensions does a bookshelf have?

Answer: A bookshelf typically has three dimensions: length, width, and height.

Q`2`. Give an example of a one-dimensional shape other than a straight line.

Answer: A ray is an example of a one-dimensional shape. 

Q`3`. What is the dimensionality of a music CD?

Answer: A music CD is typically considered to be a two-dimensional object as it has only diameter and thickness.

Q`4`. Name a real-life example of a three-dimensional object that you use every day.

Answer: A refrigerator is a common example of a three-dimensional object, as it has length, width, and height.