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It is true that both the terms, area, and volume, have large scale uses in normal day to day lives. Although we are taught about area and volume during our school days, it is important that we remember them for the rest of our lives. It is often seen that most of us often get confused by both terms.
Although area and volume may seem almost similar to most of us, it is not so at all.
Area vs Volume
The difference between Area and Volume is that area means the space which an object occupies and volume means the space which the object contains. The area has 2-dimensional shapes while volume has 3-dimensional shapes. For example, a can covers 5 cm of the area whereas the same can contains 5 liters of water which is the volume of the can.
The total space that objects occupy when placed on a plane or flat surface is known as the area of the object. Similarly, there are also some objects that have their own capacity. For example, a water tank has its own capacity of holding a certain amount of water inside.
This capacity is the volume of the water tank. It is important for you to note that only hollow objects have volumes that can be measured with relevant formulae.
The table and forthcoming information on the two terms should be able to throw some light on the topic and help you understand the basic differences between an area and a volume of an object.
Comparison Table Between Area and Volume
|Parameter Of Comparison||Area||Volume|
|Definition||Refers to the space occupied by a shape or object when placed on a flat surface.||Refers to the total capacity of an object.|
|Shapes||Simple figures.||Solids of any shape with hollow inside, such as tanks, suitcases, and glasses.|
|Measured In||Square Unit.||Cubic Unit.|
|Involves||Always involves 2 dimensional objects or shapes||Always involves 3 dimensional objects or shapes.|
What is Area?
Traveling back in time, if we go back to our mathematics classes, we were told that the area of any object is the total 2-dimensional space that is covered by an object or shape. It will not be wrong if we say that the area of an object basically tells us the amount of space that is taken up by any plane object.
This is simply calculated by multiplying the different dimensions of the given shape. It will not be wrong if we say that the area of any object will tell us the total number of squares of fixed sizes that will be required to cover up the said object.
According to the International System of Units or SI, the standard unit of an area is square meters, which is expressed in the form of m². It is important for us to note that the area of different shapes is measured with the help of different formulae. Some of the most commonly used formulae have been discussed below.
- Area of a Square: Side x Side
- Area of a Rectangle: Length x Width
- Area of a Parallelogram: Breadth x Height
- Area of a Triangle: (Breadth x Height) x 2
- Area of a Circle: πr²
What is the Volume?
When we talk about the volume of any object, it basically refers to the total quantity of 3-dimensional space that is enclosed by a closed surface.
In other words, it tells us the total amount of space that is contained in the object. The SI unit of volume is the cubic meter and is represented by m³. If we put it in a simple language, the volume of anything is just the total capacity of the object. For example, a soccer ball or even a basketball will hold a specific volume or quantity of air inside.
Just like an area of an object of different shapes, there are different formulae to measure the volume of different types of objects. These formulae have been discussed below for your benefit.
- The volume of a Cube: a³
- The volume of a Rectangular Prism: Length x Width x Height
- The Volume of a Sphere: (4/3) x π x r³
- The volume of a Cylinder: π x r² x Height
- The volume of a Cone: π x r² x (Height/3)
Main Differences Between Area and Volume
- The area always refers to a 2 dimensional or an object in a plane. On the other hand, the volume is used to define a 3-dimensional object and its individual capacity.
- Any plane figure will have an area, whereas, solid shapes will always have a volume.
- When we talk about an area of anything, it basically tells us about the amount of space enclosed by the sides of the object, which are normally the length and the breadth. At the same time, the volume means the total capacity of any solid object that involves its length, breadth, and height.
- The area of any object is measured in square units such as square centimeters or square meters or even square kilometers. However, the volume is measured in the form of cubic units such as cubic centimeters, cubic meters, and cubic grams.
- Any shape that has 2 dimensions, which are length and breadth, will always have an area. However, any shape that has 3-dimensions such as length, breadth, and height, will always have a volume.
Frequently Asked Questions (FAQ) About Area and Volume
Are capacity and volume the same thing?
Volume is the space generally occupied by an object whereas capacity means how much an object can contain or carry in itself. For instance, if you put a bottle of water on a table, it occupies the empty space on the table.
This empty space is the volume. However, the space taken by the water inside the bottle is the capacity of the bottle that how much maximum amount of water it can contain inside it.
Both capacity and volume have similar concepts but they are not the same.
What is the difference between area and surface area?
The area is a word or expression that is used in the context of the size of a two-dimensional plane like a playground. An area of a plane can be expressed in many units like square meter, hectare, acre, square kilometer, square ft, and square mile to name a few.
On the other hand, the surface can be the same if it is also used in the context of a 2D plane. But surface area generally expresses the size of the exposed surface of an object. Hence the surface area is most commonly used in the context of three-dimensional objects.
For example – A cube has a total surface area that equals the sum of the areas of all its six sides.
What are the two formulas for volume?
There are many formulas to calculate the volume of different shapes and objects.
The two most commonly used formulas are the formulas used for cuboid and prism:
- Formula to calculate the volume of the cuboid is lwh. Here l=length, w=width, and h=height.
- Formula to calculate the volume of a prism is Bh. Here B=area of base and h=height.
What is the formula for finding the area of a sphere?
The formula for finding the area of a sphere is:
A=4π × r2
In this formula, A stands for the area; π stands for pi and r stands for radius. This formula was first used by the famous Greek philosopher Archimedes about two thousand years ago.
Thanks to the above discussion, we all know by now what an area is and what a volume is. We also know the way we need to measure the areas and volumes of any object.
By now it is crystal clear the area and volume are separate mathematical concepts that differ from each other in multiple ways.
The area of any 2-dimensional object or figure refers to the space covered by any plane object. At the same time, the volume of any 3-dimensional object or figure refers to the total amount of space inside the said object.
When it comes to measuring the area of any 2-dimensional shape or object, there are different formulae used for different shapes, such as there is a separate formula for measuring the area of a square and a different formula for measuring the area of a triangle.
Similarly, there are different formulae used to measure the volume of different types of 3-dimensional figures or objects. For example, you need to use a different formula to measure the volume of a cylinder and a different formula to measure the volume of a sphere.
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