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Area and Volume

In this article, we will discuss area and volume, their definitions, how and when it is used, formulas, a comparison between both of them and the difference between area and volume.

As you can see, there are numerous items around us that have a specific area or volume that we are unaware of. While the area refers to the area covered by a closed planar figure, the volume refers to the quantity of space used by an object. The size of a room is measured in square metres, but the volume of a room is measured in cubic metres.

The phrases area and volume are two essential mensuration notions that are used widely not only in mathematics but also in everyday life. The purpose of this article is to highlight the important distinctions between area and volume.

The area of an object is defined as the area it covers, whereas the volume of an object is defined as its capacity. A two-dimensional object’s area is computed, whereas a three-dimensional object’s volume is calculated. The area corresponds to the outward space, while the volume corresponds to the internal capacity. The volume is measured in cubic units, such as cubic feet, cubic inches, and so on, whereas the area is measured in square units, such as square inches, square feet, and so on.

Any three-dimensional geometric shape’s surface area and volume can be determined. The area or region occupied by the object’s surface is referred to as the surface area. Volume, on the other hand, is the quantity of space available in an object.

There are many various forms and sizes in geometry, such as the sphere, cube, cuboid, cone, cylinder, and so on. Each form has a volume and a surface area. However, we can only measure the area covered by two-dimensional forms such as squares, circles, rectangles, triangles, and so on, and there is no volume available. Let’s look at the formulas for surface areas and volumes for various 3D shapes.

Definitions

Area

In geometry, an object’s area is simply its size or the two-dimensional space or region that a closed figure covers. It calculates the amount of space occupied by a flat object by multiplying the shape’s dimensions.

The area allows us to calculate how many squares of a fixed size would be required to cover the shape. The square metre is the standard unit of area in the International System of Units (SI) (expressed as m²). The formula for calculating the area of various objects is given below:

Formula

• Area of Square = side × side
• Area of Rectangle = l × w
• Area of Parallelogram = b × h
• Area of Triangle = (b × h) / 2

Area of Circle = πr²

where l is the length
w is the width
h is the height
b is the base

Volume

The amount of space inside a three-dimensional object enclosed by a closed surface is referred to as volume, and it indicates how much space the shape includes. The SI unit of volume is the cubic metre.

In simple words, an object’s volume is equal to its capacity. Assume there is a hollow bottle with a volume equal to the amount of liquid it can hold. The formula for the volume of various things is given below:

Formula

• Volume of Rectangular Prism = l × w × h
• Volume of Cube = a³
• Volume of Sphere = (4/3) × π × r³
• Volume of Cylinder = π × r² × h
• Volume of Cone = π × r² × (h/3)

where l is the length
w is the width
h is the height
a is edge
h is the height

Area and Volume: Key Differences

In terms of the difference between area and volume, the following points are important:

1. The area of a flat figure or object refers to its region or space. The volume of an object is the amount of space it occupies.
2. Solid shapes have volume, whereas plane figures have area.
3. The quantity of space enclosed is described by area, whereas the capacity of solids is determined by volume.
4. Area is measured in square units, which can be centimetres, yards, or other measurements. The volume, on the other hand, is measured in cubic units.
5. Area refers to shapes with two dimensions, such as length and width. Shapes with three dimensions, such as length, width, and height, on the other hand, have volume.

Conclusion

As a result of the preceding discussion, you may have realised that the two mathematical notions differ significantly in their application and measurement. While the area is used to identify how much space a planar object covers, the volume is used to establish how much space is inside the item.

Get answers to the most common queries related to the JEE Examination Preparation.

What is the relationship between volume and area?

Answer: The area of a flat figure or object refers to its region or space. The volume of an object is the amo...Read full

What is the difference between volume and area?

Answer: A two-dimensional item is an area, whereas a three-dimensional object is a volume. Volume is a solid ...Read full