Difference Between Area and Volume
The area is defined as the region covered by the object., whereas volume is defined as the capacity of the object. Area is calculated for a two-dimensional object whereas volume is calculated for a three-dimensional object. The area is linked to the outer space and volume to the inner capacity. The area is measured in square units, such as square inches, square feet, etc, and volume is measured in cubic units, such as cubic feet, cubic inches, etc.
In this article, let us explore the difference between area and volume with solved examples and practice questions.
|1.||What is area and Volume?|
|2.||Difference Between Area and Volume|
|3.||Area and Volume Formulas|
|4.||Examples on Difference Between Area and Volume|
|5.||FAQs on Difference Between Area and Volume|
What is Area and Volume?
Area refers to the amount of space occupied by a two-dimensional figure/object. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units, generally represented as square inches, square feet, etc.
Volume refers to the measure of the capacity that an object can hold. It can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The standard unit of area is cubic units, generally represented as cubic inches, cubic feet, etc.
Difference Between Area and Volume
The important differences between area and volume are listed in the table given below.
Area vs Volume
|Area is always defined for two dimensions objects or plane figures.||Volume is always defined for three-dimensional objects or solid figures.|
|It is measured in 2 dimensions, includes mainly length and width.||It is measured in 3 dimensions, includes the third dimension, which is height.|
|It is measured in square units||It is measured in cubic units|
|The area covers the outer space of an object.||Volume is the capacity of an object.|
Area and Volume Formulas
The area and volume formulas for different two-dimensional and three-dimensional shapes are listed in the tables given below.
Area Formula Chart for 2D shapes
|Geometric shapes||Area formula|
|Square||A = a2 (a = side of square)|
|Rectangle||A = l × w (l = length, w = width)|
|Triangle||A = ½ x b x h (b = base, h = height)|
|Parallelogram||A = b × h (b = base, h = vertical height)|
|Rhombus||A = a × h (a = side of rhombus, h = height)|
|Circle||A = π r2 (r = radius of circle)|
|Semi-circle||A = π r2 (r = radius of circle)|
|Trapezoid||A = ½ (a + b)h (a = base 1, b = base 2, h = vertical height)|
Volume Formula Chart for 3D Shapes
|Geometric shapes||Volume formula|
|Cube||V = a3 (a = side of square)|
|Cuboid||V = l × w × h (l = length, w = width, h = height)|
|Right Circular Cone||V = 1/3 (π r2 h) (r = radius of circular base, h = height of cone)|
|Right Circular Cylinder||V = π r2 h (r = radius of circular base, h = height of cylinder)|
|Right Pyramid||V = 1/3 (Area of base) × height|
|Right Prism||V = Area of base × height|
|Sphere||V = 4/3 (π r3) (r = radius of sphere)|
|Hemisphere||V = 2/3 (π r3) (r = radius of hemisphere)|
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Examples on Difference Between Area and Volume
Example 1: The dimensions of a rectangle are 10 cm and 8 cm. Find its area.
The area of a rectangle is the product of its length and width, which can be represented by the formula: Area = l × w.
Substituting the given values, we get area of the rectangle = 10 × 8 = 80 cm2
Therefore, Area of the rectangle is 80 cm2
Example 2: Determine the volume of the conical vessel with a radius of 7 inches and a height of 9 inches. Use π = 22/7.
The vessel is in the shape of a cone.
Volume of cone = 1/3 π r² h = 1/3 × 22/7 × 7 × 7 × 9 = 462 in3.
Therefore, Volume of the vessel is 462 in3.
FAQs on Difference Between Area and Volume
What Is the Difference Between Area and Volume?
The important points of differences between area and volume.
- The area is defined as the region covered by the object., whereas volume is defined as the capacity of the object.
- Area is calculated for a two-dimensional object whereas volume is calculated for a three-dimensional object.
- The area is measured in square units and volume is measured in cubic units.
What Is the Difference Between Area, Perimeter, and Volume?
The area refers to the space occupied by the shape while the perimeter refers to the distance around the shape(the boundary of the shape) and volume refers to the capacity of the given three-dimensional shape.
How Is Area Related to Volume?
Surface area is basically the area of the object exposed to the outside, whereas, volume is the space inside the shape.
What Is the Area of a Triangle?
The area of a triangle is the total space occupied by its three sides in a 2-dimensional plane. The formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. it is applicable to all types of triangles - a scalene triangle, an isosceles triangle, or an equilateral triangle. Note that in the case of a triangle, the base and the height are perpendicular to each other.
How To Find the Area of a Circle?
The area of a circle refers to the space occupied by the circle in a two-dimensional plane. In other words, it is the space occupied within the boundary of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, for example, m2, cm2, in2, etc.
What Is the Volume of a Cylinder?
The volume of a cylinder refers to the space occupied by the cylinder in a three-dimensional plane. The formula for the area of a cylinder is A = πr2h, where 'r' is the radius of the base (circle) of the cylinder, 'h' is the height of the cylinder and π is a constant whose value is either 22/7 (or) 3.142. It is measured in cubic units such as cm3, m3, in3, etc.