Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
Dimensions are generally expressed as:
- Height or Depth
Types of Figures Based on Dimensions
Based on the number of dimensions present in a figure, it can be classified into:
- Zero – dimensional
- One – dimensional
- Two – dimensional
- Three – dimensional
- Zero – dimensional
A point is a zero-dimensional object as it has no length, width or height. It has no size. It tells about the location only.
Only a single measurement is possible for a one-dimensional figure. A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
The 2-dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width. Two-dimensional or 2-D shapes do not have any thickness and can be measured in only two faces.
The two dimensions are marked on a 2-D graph with two axes: x and y. The x-axis is perpendicular or at 90° to the y-axis.
In geometry, three-dimensional shapes are solid figures or objects or shapes that have three dimensions – length, width, and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
A cube and cuboid are examples of three-dimensional objects, as they have length, width, and height.
Take for example a cuboid,
The attributes of the cuboid are faces, edges, and vertices. The three dimensions compose the edges of a 3D geometric shape.
Some Examples of Three-Dimensional Shapes:
When the three dimensions are marked on a graph, a 3-D graph has three axes, namely, x, y, and z. Each axis is perpendicular or at 90° to the other.
Solved Examples On Dimensions
Question 1: How many dimensions does the given figure have?
Answer: The figure is a curved line drawn from one point to another and has only one dimension, length.
Question 2: How many dimensions does the given figure have?
Answer: This is a dot or a point. It has no dimension at all, with no length, breadth, or width.
Question 3: How many dimensions does a scale have?
Answer: A scale has a length, a breadth, and thickness. Therefore, it can be said to be three-dimensional.
Question 4: How many dimensions does a cylindrical water bucket have?
Answer: A cylindrical bucket has a height, depth, and width. Thus, it is a three-dimensional figure.
Practice Problems On Dimensions
How many dimensions does the object have?
The Rubix cube has a length, breadth, and width. It is three-dimensional.
How many dimensions does the given figure have?
The figure is a circle with a length and a width measured between two points on the circle.
What is the dimensional type of an object which has only a length?
An object having only one measurement is one-dimensional.
How many dimensions does a notebook have?
A notebook has length, breadth, and width. So, it is three-dimensional.
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Frequently Asked Questions On Dimensions
What is a three-dimensional square?
A cube is a square drawn in a three-dimensional manner. A square has only length and breadth, but a cube has length, breadth, and width.
What is it called when an object has no dimensions at all?
It is a zero-dimensional figure, and it cannot be an object. It is a mere point on a surface with no length or breadth to measure.
How can you express the dimensions of your room?
The room is a three-dimensional structure. It should have:
- A length measured along the floor
- A height measured from floor to ceiling
- A width measured along the floor, adjacent to length.