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.
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(A zero-dimensional shape)
`2`. One-dimensional shape: A one-dimensional shape has only length. A line segment is a one-dimensional shape.
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(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?
- Sphere
- Cylinder
- Triangle
- Cube
Answer: c
Q`2`. In geometry, which of the following is an example of a one-dimensional object?
- Square
- Line segment
- Triangle
- Circle
Answer: b
Q`3`. Among the given options, which represents a real-life three-dimensional object?
- Mirror
- Basketball
- Bookmark
- String
Answer: b
Q`4`. What is the dimensionality of an aquarium?
- `0` Dimension
- `1` Dimension
- `2` Dimensions
- `3` Dimensions
Answer: d
Q`5`. Which of the following mathematical concepts is considered to have no dimensions?
- Point
- Line
- Circle
- 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.