Difference Between Area and Volume – Definition, Formulas, FAQs

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What Is the Difference between Area and Volume?

Area and volume of shapes are two fundamental measurements in geometry. Area is the measure of the space covered by a flat 2D surface, like the floor of a room. Volume, on the other hand, is the measure of the space occupied by a three-dimensional object, like a box.

Area vs. volume

While area is expressed in square units (like square inches), volume is expressed in cubic units (like cubic inches). In simple terms, area deals with the surface space, while volume deals with the space inside an object.

What Is Area?

Area is defined as the total space taken up by a flat (2D) surface or shape of an object.

Definition of Area in Geometry: The space enclosed by the boundary of a plane figure is known as its area. The area of a figure is the number of unit squares that perfectly cover the surface of a closed figure. 

Area is measured in square units like square inches, square yards, etc. Area of a shape is a two dimensional quantity. 

If you want to paint a 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.

What Is Volume?

Every three-dimensional object occupies some space. This space is measured in terms of its volume. 

Definition of Volume in Geometry: Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. 

Volume refers to the three-dimensional space inside an object, while capacity specifically refers to the amount a container can hold.

When building a fish tank, understanding the Volume of the tank helps determine how much water it can hold and what size of a filter or pump is needed.

Difference Between Area and Volume

AreaVolume
It is defined for two dimensional shapes.It is defined for three dimensional objects.
Area refers to the space taken up by a flat, two-dimensional shape on a surface. Volume pertains to the amount of space occupied by a three-dimensional object.
It is expressed in square units like square inches, square feet, etc. It is expressed in cubic units like cubic inches, cubic feet, etc. 
Examples of 2D shapes: quadrilaterals, circles, polygons, etc.Examples of 3D shapes: cube, cuboid, sphere, etc. 

Formulas for Area and Volume

The area and volume formulas for different two-dimensional and three-dimensional shapes are listed in the tables given below. Calculating area and volume becomes easier once you know the required dimensions. Just substitute the values in the formula and assign the appropriate unit.

Area Formula Chart for 2D shapes

Geometric shapesDimensionsArea formula
Squarea = side of squareA $= a^{2}$
Rectanglel = length, w = widthA $= l \times w$
Triangleb = base, h = heightA $= \frac{1}{2} \times b \times h$ 
Parallelogramb = base, h = heightA $= b \times h$ 
Rhombusa = side of rhombus, h = heightA $= a \times h$
Circler = radius of circleA $= \pi r^{2}$ 
Semicircler = radius of semicircleA $= \frac{1}{2} \pi r^{2}$
Trapezoida and b = bases, h = heightA $= \frac{1}{2} \times (a + b) \times h$ 

Volume Formula Chart for 2D shapes

Geometric shapesDimensionsVolume formula
Cubea = side of squareV $= a^{3}$
Cuboidl = length, w = width, h = heightV $= l \times w \times h$ 
Right Circular Coner = radius of circular base, h = height of coneV $= \frac{1}{3} \pi r^{2}h$ 
Right Circular Cylinderr = radius of circular base, h = height of cylinderV $= \pi r^{2}h$ 
Spherer = radius of sphereV $= \frac{4}{3} \pi r^{3}$ 
Hemispherer = radius of hemisphereV $= \frac{2}{3} \pi r^{3}$
Right PyramidV $= \frac{1}{3} \times$ (Area of base) $\times$ height
Right PrismV = Area of base $\times$ height

Facts about Difference between Area and Volume

  • Area pertains to two-dimensional space within a flat shape.
  • Volume involves the capacity occupied by a three-dimensional object.
  • Area is measured in square units (e.g., square inches, square meters).
  • Volume is measured in cubic units (e.g., cubic centimeters, cubic feet).
  • Area is used for measuring surfaces like walls, floors, and 2D shapes.
  • Volume is used for measuring capacity, such as the contents of a container or 3D objects.

Conclusion

In this article, we explored the distinction between area and volume, understanding that area refers to the space within a flat shape while volume encompasses the capacity of a three-dimensional object. Let’s check our understanding by attempting practice exercises and solving examples.

Solved Examples on Difference between Area and Volume

1. The dimensions of a rectangle are 12 inches and 9 inches. Find its area.

Solution

Length = 12 inches

Breadth = 9 inches

Area = Length $\times$ Breadth

Area = 12 $\times$ 9 

Area = 108 square inches

2. What is the volume of the cone whose base radius is 7 feet and height is 12 feet?

Solution

Base Radius (r) = 7 feet

Height (h) = 10 feet

Volume of the cone $= \frac{1}{3} \pi r^{2}h$

Volume of the cone  $= \frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 12$ 

Volume of the cone = 616 cubic feet

3. Find the area of a triangle with base 3 feet and height 6 feet. 

Solution

Base (b) = 3 feet

Height (h) = 6 feet

Area $= \frac{1}{2} \times b \times h$

Area $= \frac{1}{2} \times 3 \times 6 = 9$ square feet

4. The radius of a sphere is 10.5 inches. Find the volume of the sphere.

Solution

Radius (r) = 10.5 inches

Volume of the sphere $= \frac{4}{3} \pi r^{3}$

Volume of the sphere $= \frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$

Volume of the sphere = 4851 cubic feet

5. A square with side 2 inches is cut out from a corner of a larger square sheet of side 6 inches. Find the area of the remaining square sheet.

Solution: 

Side of large square = 6 inches

Area of the large square $= 6 \times 6 = 36$ square inches

Side of small square = 2 inches

Area of the small square $= 2 \times 2 = 4$ square inches

Area of the remaining sheet = Area of the large square – Area of the small square

Area of the remaining sheet = 36 – 4 = 32 square inches

Practice Problems on Difference between Area and Volume

Difference Between Area and Volume - Definition, Formulas, FAQs

Attend this quiz & Test your knowledge.

1

What is area?

The space occupied by a three-dimensional object.
The capacity of a container.
The amount of space occupied by a two-dimensional shape.
The length and width of an object.
CorrectIncorrect
Correct answer is: The amount of space occupied by a two-dimensional shape.
Area is the amount of space occupied by a two-dimensional shape.
2

What does volume measure?

Total region covered by its outer surface
The thickness of an object.
The space occupied by a three-dimensional object.
The lateral surface area of 3D object
CorrectIncorrect
Correct answer is: The space occupied by a three-dimensional object.
Volume measures the space occupied by a three-dimensional object.
3

Which of the following objects have a volume?

paper sheet
floor tile
Tuna can
TV screen
CorrectIncorrect
Correct answer is: Tuna can
A can of tune is a 3D object (usually comes in cylindrical shape). It has volume. All the other options are 2D shapes.
4

Area of rectangle =

$Length \times Breadth$
$Length \times Breadth \times Height$
$Length^{2}$
$2(Length + Breadth)$
CorrectIncorrect
Correct answer is: $Length \times Breadth$
Area of the rectangle $= Length \times Breadth$
5

If area of base of a right pyramid is 9 square feet and height is 15 square feet, the volume will be :

45 cubic feet
25 cubic feet
90 cubic feet
105 cubic feet
CorrectIncorrect
Correct answer is: 45 cubic feet
Area of base (A) = 9 square feet
Height (h) = 15 square feet
V $= \frac{1}{3} \times$ (Area of base) $\times$ height
V $= \frac{1}{3} \times 9 \times 15 = 45$ cubic feet

Frequently Asked Questions on Difference between Area and Volume

Perimeter is the length of the boundary of a two dimensional shape whereas Area is the space occupied by a two dimensional shape or object.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

Area is the space occupied by a two dimensional object whereas surface area is the total area of the outer surfaces of an object.

Area is the space inside a 2D shape, while volume is the space occupied by a 3D object.