Difference between Area and Volume

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An important difference between area and volume depends upon the region covered by the object. Area is used for calculating two-dimensional objects, whereas volume is used for calculating a three-dimensional object.

Finding the key difference between area and volume is essential in the field of geometry.
As we know, geometry is the study of shapes, dealing with solid and plane shapes.
We calculate various terms associated with shapes, such as height, volume, width, area, perimeter, length, etc.
Area and volume are two essential concepts used in our daily life.
We see many shapes around, like circles, squares, polygons, rectangles, etc.
Every shape has its unique measurements and properties.
Therefore, each shape has a different area and volume, depending on its measurement.

Table of Content

What is Area?
What is Volume?
What is the differences between Area and Volume?
Difference of Area and Volume of Shapes
Things to Remember
Sample Questions

Key Terms: Difference between Area and Volume, Area, Volume, Geometry, Circles, Square, Polygons, Rectangles, Difference of Area and Volume of Shapes, Parallelogram, Hexagon

What is Area?

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The area is the measurement of the region covered by any 2-dimensional geometric shapes. Every shape has different areas. For instance, the area of a square is different from the area of a rectangle.

It is linked to the outer space.
The area of a shape is calculated in square (sq) units such as square inches, square feet, etc
It is used to measure the number of unit squares that cover the surface of a closed figure.
If two figures have similar shapes, they don't need to have the same area unless they have the same dimension.
The 2D shapes include square, circle, hexagon, rectangle, pentagon, triangle, parallelogram, etc.
Therefore, all these figures have different areas.

Example of What is Area?

Example: We can see an example, if you want to paint a rectangular wall of your house, then you need to know the area of a wall so that you know how much amount of paint is required to paint the wall to calculate the cost of painting.

Also Read:

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Area of Triangle	Areas Related to Circles	Perimeter and Area of a Circle
Surface Areas and Volumes	Area of Segment of a Circle	Surface Area of a Cone Formula

What is Volume?

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The volume of an object is defined as the measurement of the amount of space occupied by a 3-dimensional object. It is the product of all three dimensions and is expressed in cubic units.

For each 3-dimensional shape, such as cylinder, cube, cone, sphere, cuboid, etc., the volume is different.
The capacity of an object is the volume of the substance that its interior can accommodate.
The interior of the object can accommodate is called the capacity of the hollow.
It is measured by counting the number of unit cubes it contains.

Example of What is Volume?

Example 1: Suppose the volume of a cube is measured by the product of its height, length, and breadth. The interior of a hollow object can be filled with a liquid or air that takes the shape of the object.

Example 2: How much oil can be stored in a cylindrical vessel having a radius of 2m, and height 7m?

Ans: Radius of the cylinder = 2m

Height of the cylinder = 7 m

Volume of the cylinder = π r² h

Volume = 22 X2 X2 X 7/ 7

Volume = 88 m³

1 m³ = 1000 l

88 m³ = 88000 L

What is the differences between Area and Volume?

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Some of the differences between area and volume in mathematics are:

Area	Volume
The area is defined as the space occupied by a 2-dimensional object.	The volume is the amount of space occupied by a 3-dimensional object.
It is expressed in a square unit.	It is expressed in the cubic unit.
This is a plane figure.	This is a solid figure.
The area covers outer space.	The volume covers the inner capacity.
It is calculated for 2 dimensions.	It is measured in 3 dimensions, i.e. Length, breadth, and height.
Examples: circle, square, rectangle, etc.	Examples: cube, sphere, cylinder, etc.

Difference of Area and Volume of Shapes

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Let us look at the areas of different shapes here:

Name of the shapes	Variables	Area of the shape
Triangle	B = base H = height	\(\frac{1}{2}\) × base × height
Trapezoid	a = base 1 b = base 2 h = vertical height	\(\frac{1}{2}\) (sum of parallel side) × height
Semicircle	r = radius of the circle	\(\frac{1}{2} \pi r^2\)
Rhombus	a= side of the rhombus h = height	a × h
Circle	r = radius of the circle= 22/7 or 3.1416	πr²
Square	a = sides of the square	a²
Rectangle	l = length w = width	l × w
Parallelogram	a = side b = base h = vertical height	b × h

Now, let us look at the volume of different shapes here:

Name of the Shape	Abbreviation Used	Volume
Sphere	r = radius	4/3πr³
Right circular cylinder	r = radius h = height	πr²h
Right circular cone	r = radius l = length	\(\frac{1}{2}\)πr²h
Cube	a = length of the side	a³
Cuboid	l = length b = breadth h = height	l × b × h
Hemisphere	r = radius	\(\frac{2}{3}\)(πr³)
Right pyramid	-	\(\frac{1}{3}\) (Area of the base) × height
Right prism	-	Area of base × height

Also Read:

Related Articles
Surface Area of a Cylinder Formula	Area of Similar Triangles	Quadrilateral Formulas
Surface Area of Cone	Volume of Sphere	Surface Area of A Hemisphere

Things to Remember

Difference between area and volume measurement of the region covered by the figure.
Area can be defined mainly for 2D figures, such as triangles, trapezoids, Semicircles, rhombus, circles, and Parallelograms.
Volume can be defined for 3D figures, such as Spheres, right circular cylinders, right circular cones, Cubes, Cuboids, Hemispheres and right prism.
We can define an area for three dimensional objects, but it would be a surface area, which is known as the area of the surface of 3D figures.
Volume is used in determining the density, mass, and properties of objects and substances.

Sample Questions

Ques: What is the volume of the cube if the edge length is 10cm? (2 marks)

Ans: We have, edge length, a = 10cm

Volume of cube = a³ [Formula]

So, volume of cube = 10³

= 10 ×10 × 10 = 1000

So, the volume of the cube is 1000cm³.

Ques: What is the area of a rectangle with a length of 10 cm and a width of 5 cm? (2 marks)

Ans: We have, length of rectangle = 10cm

Width of rectangle = 5 cm

Area of the rectangle = length × width [Formula]

So, the area of the rectangle = 10 × 5

= 10 × 5 = 50

So, the area of the rectangle is 50cm².

Ques: What is the volume of a cubic box if its side is 8cm? (2 marks)

Ans: We have, side of the box, a = 8cm

Volume of cube = a³ [Formula]

So, volume of cube = 8³

= 8 × 8 × 8 = 512

So, the volume of cubic box is 512cm³.

Ques: What is the area of a square plot if the side is 7cm? (2 marks)

Ans: We have, side of the square plot, s = 7cm

Area of square = a² [Formula]

So, area of square = 7²

= 7 × 7 = 49

So, the area of the square plot is 49cm.

Ques: Is the cube a square? (2 marks)

Ans: A square is a two-dimensional shape that has w dimensions of length and breadth, while a cube is a 3-dimensional shape that has 3 dimensions of height, length, and breadth. The side faces of a cube are formed by the square and it has 4 verticals and 4 sides, while a cube has 8 verticals and 12 sides. From these properties, we can say that the basic difference between a cube and a square is of dimensions.

Ques: What is the volume of a sphere having a radius of 3 cm? (3 marks)

Ans. Radius of sphere r = 7cm

Volume of a sphere = V = 4πr³/3 cubic units

V = 4/3 × 3.14 × 7³

V = 4/3 × 3.14 × 7 × 7 × 7

V = 1436.04 cm³

Hence the volume of given sphere is 1436.04 cubic cm.

Ques: Calculate the area of the triangle whose base is 21 cm and height is 10 cm? (2 marks)

Ans: Area of a triangle = ½xbxh
Given, base = 21 cm & height = 10 cm
Area = ½ x 21 x 10 = 105 cm².

Ques: Calculate the breadth of a rectangular plot of land, if its area is 360 square meters and the length is 120 m? (2 marks)

Ans. Area = 360 square m (given)

Length (l) = 120 m
Area of a rectangle = l x b
360 = 120 x b
b = 360/120 = 3 m

Ques: From a rectangular sheet of paper of dimensions 9 cm × 4 cm, a square piece of dimension 1 cm × 2 cm. What will be the ratio of the areas of the two figures? (3 marks)

Ans: Length = 9 cm
Breadth = 4 cm
Area of the sheet = l × b = 9 cm × 4 cm = 36 cm²
Area of the square piece = 1 cm × 2 cm = 2 cm²
Ratio of areas of two figures = 36 cm² : 2 cm² = 18 : 1

Ques: Two cubes of edge 4 cm are joined to form a cuboid. Find the total surface area of the cuboid? (2 marks)

Ans: When two cubes are joined end to end, then

Length of the cuboid = 4 + 4 = 8 cm

Breadth of the cuboid = 4 cm

Height of the cuboid = 4 cm

Total surface area of the cuboid = 2 (lb + bh + hi)

= 2(8 x4 + 4×4 + 4×8)

= 2(32 + 16 + 32) = 2(80) = 160 cm²

Ques: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 12 m? (Assume π = 22/7) (2 marks)

Ans: Radius of cone, r = 12/2 m = 6m

Slant height, l = 21 m

Formula: Total Surface area of the cone = πr(l+r)

Total Surface area of the cone = (22/7)×6×(21+6) m²

= 509.14m²

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Difference between Area and Volume

What is Area?

Example of What is Area?

What is Volume?

Example of What is Volume?

What is the differences between Area and Volume?

Difference of Area and Volume of Shapes

Things to Remember

Sample Questions

CBSE X Related Questions

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

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Difference between Area and Volume

What is Area?

Example of What is Area?

What is Volume?

Example of What is Volume?

What is the differences between Area and Volume?

Difference of Area and Volume of Shapes

Things to Remember

Sample Questions

CBSE X Related Questions

1.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.