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Difference Between Area and Volume

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Last updated date: 19th May 2024
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Area vs Volume

As we know that geometry is the study of Shapes. It deals with plane Shapes and solid Shapes. We calculate different terms associated with the Shapes, like length, width, height, Area, perimeter, Volume, etc. Area and Volume are the two important concepts used in our daily life. We see many Shapes around like squares, rectangles, circles, polygons, etc. Every Shape has its unique properties and measurements. Hence every Shape has a different Area and Volume, based on their measurements. So here on this page, we will study the difference between Area and Volume in Math and formulas associated with different Shapes.


Area

The Area is the measurement of the region covered by any two-dimensional geometric Shapes. The Area of any Shape depends upon its dimensions. Different Shapes have different Areas. For instance, the Area of the square differs from the Area of the rectangle. The Area of a Shape is calculated in square units (sq units). 


Suppose if you want to paint the rectangular wall of your house, you need to know the Area of the wall to calculate the quantity of the paint required to paint the wall and the cost of painting.


If two figures have a similar Shape it is not necessary that they have equal Area unless and until their dimensions are equal. Suppose two squares have sides s and s1, so the Areas of the two square will be equal if s = s1


Volume

The space occupied by the three-dimensional object is measured in terms of the Volume of that object. The Volume of a solid Shape is the product of three dimensions, so the Volume is expressed in cubic units. Suppose the Volume of a cube is measured by the product of its length, width, and height.


The interior of a hollow object can be filled with air or some liquid that takes the Shape of the object. In such cases, the Volume of the substance that the interior of the object can accommodate is called the capacity of the hollow object. Thus we may say that the Volume of an object is the measure of the space it occupies and the capacity of an object is the Volume of the substance its interior can accommodate.


Area vs Volume Definition

The Area refers to the region covered by the object. And Volume refers to the quantity or capacity of the object. An Area is a two-dimensional object whereas Volume is a three-dimensional object. The Area is a plain figure while Volume is a solid figure. The Area covers the outer space and Volume covers the inner capacity. The Area is measured in square units and Volume is measured in cubic units. 


Generally, the Area is calculated for two-dimensional objects, while Volume is calculated for three-dimensional objects.


Here is the pictorial representation of Area and Volume which shows the relation between Area and Volume.


(Image will be Uploaded Soon)


Let us try to understand the relation between Area and Volume and the difference between Area and Volume in detail.


Area Formula Chart for 2D Shapes

Name of Geometric Shapes

Area Formula

Variables

Rectangle

Area = l \[\times\] w

l =  length

w  = width

Square

Area  = a2

a = sides of the square

Triangle

Area = ½ \[\times\] b \[\times\] h

b = base

h = height

Trapezoid

Area = 1/2 (a + b)h

a =base 1

b = base 2

h = vertical height

Parallelogram

Area  = b \[\times\] h

a = side

b=base

h=vertical height


Rhombus

Area = a \[\times\] h

a = side of rhombus

h = height

Circle

Area = πr2

r = radius of the circle

= (22)/7 or 3.1416

Semicircle

Area = ½ πr2


r = radius of the circle


Volume Formula Chart for 3D Shapes(Solid Shapes)

Name of Geometric Shapes

Volume Formula

Abbreviations Used

Cuboid

L \[\times\] b\[\times\] h 

h = height, 

l = length  b=breadth

Cube

a3

a = length of the sides

Right Prism

Area of Base \[\times\] Height

..

Right Circular Cylinder

πr2h

r= radius

h=height

Right pyramid

⅓ (Area of the Base) \[\times\] Height

..

Right Circular Cone

⅓ (πr2h)

r = radius

l = length

Sphere

4/3πr3

r = radius

Hemisphere

⅔ (πr3)

r = radius


Difference Between Area and Volume

Some of the key difference between Area and Volume in Math are:


Area vs Volume

The Area is the measurement of the region covered by any two-dimensional geometric Shapes.

The Volume is the space occupied by the three-dimensional object.

The Area is measured for plain figures

Volume is measured for 3D(solid) figures.

The Area is measured in two dimensions i.e length and breadth.

Volume is measured in three dimensions i.e length, breadth, and height.

The Area is measured in square units 

Volume is measured in cubic units.

The Area covers the outer space of an object 

Volume is the capacity of an object

Example: square, rectangle, circle, etc.

Example: cube, cuboid, sphere, etc.


These differences show the relation between Area and Volume. As now the difference between Area and Volume in Math is clear, let us solve some examples.


Solved Examples

1. The sides of a square plot is 9m.  Find the Area of a square plot.

Ans:  Given, Side = a = 9m

By the formula of Area of a square, we know that

Area = a2

A = 9 x 9

A = 81 sq.m.or 81


2. The side of the cubic box is 9m. Find the Volume of a cubic box.

Ans: Given, Side = a = 9m

By the formula of Volume of a cube, we know that

V = a3

V = 9 x 9 x 9

V = 729 sq.m or 729m2


Area and Volume of an object both are dependent on the dimension of a particular Shape or figure. While Area is the amount of space the object, figure occupies in a two dimensional space, Volume is the capacity of a Shape or figure in three dimensional space. Area of a Shape is the amount of space that an object takes and Volume may be defined as the capacity or amount of space than an object or Shape has in it. Both are and Volume are important in determining the aspects and estimations in Mathematics, designing and engineering. Area is related to both planes and solid Shapes while Volume is only calculated for solid Shapes. The amount of paint to be used while painting a room can be estimated by calculating the Area of that room but the amount of air the room has or the amount of water that can be contained in that room can be estimated by calculating the Volume of that room. This means that Area and Volume may be closely related yet exist in completely different dimensions of space.


Area of a solid Shape from a particular side or direction can be explained as the shadow of that solid figure on a particular plane. Eg On a particular plane, the shadow of a sphere from any direction or side is a circle and thus the Area of the sphere from a particular direction is the Area of a circle with the diameter equal to the diameter of the sphere. However, the total surface Area of a sphere is a separate quantity and is equal to the Area of four such circles when seen from four perpendicular directions. Similarly for a cube, the Area of one face of the cube is equal to the Area of a square whose side is equal to the side of the particular cube. The Area of a cone when seen from a side i.e direction perpendicular to the height of the cone will appear to be equal to the are of the triangle having respective dimension of the cone but if seen from the top or bottom the Area of the cone from that particular direction is the Area of the circle with radius equal to the radius of the cone. 


The Volume of the solid Shapes is irrespective of the direction from which they are analyzed. The Volume of the cube has a fixed value no matter from which direction one may analyze it. The cube will have the same capacity and will take the same amount of space in the three dimensional geometry. The various formulas for calculation of Area, total surface Area and Volume of different Shapes and solids are shown in the tables above. As is evident from the table, the Area is a two dimensional concept and accordingly has the unit of (Length)2., on the other hand the Volume is a three dimensional concept and hence has a unit of (Length)3


How are Area and Volume Related?

Area and Volume are related in the sense that extension or expansion or rotation of two dimensional Areas in another (third) dimension will result in the formation of a solid figure which has a Volume. Eg the expansion of a circle along the height dimension will result in the formation of a cylinder, the expansion of a square will result in the formation of a cube of certain Volume, the rotation of a triangle along any of its axis will result in the formation of a cone of certain Volume.


Can One calculate Volume from Area?

There are certain figures which have a single parameter which is required for the calculation of both Area and Volume of an object. Thus if one knows one among  the Area or Volume of the object one can calculate the other one. E.g the sphere has a parameter of radius and using that one can calculate both Area and Volume of the sphere, or if one knows one among the Area of the sphere or the Volume of the sphere one can calculate the other one.


However this is not possible for all the figures. The frustum or the cone do not follow the same pattern because one requires two different parameters for calculation of Area and Volume, thus even if one is among the Area or the Volume of the cone, onecan’t calculate the other unless one also knows one of the two parameters of the figures.


Where is the Area and Volume Required in Daily Life?

It is Often required to calculate the Area and Volume at multiple instances in our day to day life. When estimating  the carpet required for the floor of our room, calculate the Area of the floor to know the Area of carpet. When the tailor has to estimate the amount of cloth required to make a garment an approximate estimation of the Area of the body is required. Similarly when buying a water tank for water storage, calculation of the Volume of the water tank is done.

FAQs on Difference Between Area and Volume

1. What is the Difference Between Area and Perimeter?

Area is defined as the space occupied by the shape. While perimeter id defined as the distance around the shape(the boundary of the shape)

 

Shapes with the same area can have different perimeters and the shapes with the same perimeter can have different areas. The area is measured in square units and the perimeter is measured in linear units. The area can be measured for 2 - dimensional objects while the perimeter is measured for one-dimensional shapes.

 

The below figure represents the difference between area and perimeter.

 

(Image will be Uploaded Soon)

2. Is Cube a Square?

The basic differences between cube and square are of dimensions. A square is a two-dimensional figure with two dimensions length and breadth, while a cube is a three-dimensional figure with three dimensions length, breadth, and height.

 

The side faces of a cube are formed by squares. The square has four sides and four vertices, whereas the cube has 12 edges(sides) and 8 vertices.

 

From these properties we can say the cube is a 3-dimensional figure formed by the square-shaped faces.

 

(Image will be Uploaded Soon)