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Difference Between Area and Surface Area for JEE Main 2024

JEE Main

Difference Between

Maths

Difference Between Area And Surface Area

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Area vs Surface

Geometry is the study of shapes. It is broadly classified into two types: plane geometry and solid geometry. Plane geometry deals with two-dimensional figures like squares, circles, rectangles, triangles, and many more whereas Solid geometry deals with the study of three-dimensional shapes like cube, cuboid, cylinder, cone, sphere, and many more.

The study of this shape is needed to find lengths, widths, area, surface area, volume, perimeter, and many more terms. Students always get confused between the terms area and surface area. They seem to be similar but they are different concepts. The area is a two-dimensional measurement while the surface area is a three-dimensional measurement. In this article, let us discuss the area definition, surface area definition, and the difference between area and surface area in detail.

Area Definition

Area definition states that -

The area is the measurement of the space occupied by any two-dimensional geometric shape. 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). As the area is measured for a two-dimensional object it has two dimensions length and width.

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 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 squares will be equal if, s = s1.

The formula for Area is a product of length and width.

Surface Area Definition

Surface area definition states that -

The surface area is the area calculated for the three-dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure. Cubes, cuboids, cones, cylinders are some of the three-dimensional objects. Therefore to find the surface area of such 3D objects we have to add the area of all its faces. We can use the basic area formula to calculate its faces as they are simple 2D figures,

For example, a cube has six faces. Therefore, its surface area will be the sum of the areas of all six faces. Since all the sides of a cube are squares, we can express the surface area of a cube as 6 x (Area of a square)

Basically, the surface area can be classified as:

Curved Surface Area (CSA)

The curved surface area of an object is the area of all the curved surfaces in an object. For a right circular cylinder, The surface joining the two bases of a right circular cylinder is called its curved surface.

Lateral Surface Area (LSA)

The lateral surface of an object is the area of all the faces of the object, excluding the area of its base and top. For a cube, the lateral surface area would be the area of four sides.

Total Surface Area (TSA)

Total surface area is the area of all the faces including the bases. For a right circular cylinder, the sum of the lateral surface area or curved surface area and the base areas of both the circles will give the total surface area of the right circular cylinder.

The area is the measure of a 2-dimensional object, for instance, we have to paint a side square wall of a hall. A house is a 3d object but we are only interested in the area of the wall. The surface area is the 2-dimensional measure of the outside of something. For instance, by measuring the surface area of your hall we can determine the amount of paint needed to paint all the walls.

So let us understand the difference between area and surface area in detail.

Key Differences Between Area and Surface Area

Now let us study the relation between area vs surface area.

The differences between area and surface area are given as :

Area vs Surface Area

Area	Surface Area
The area is the measurement of the space occupied by any two-dimensional geometric shape.	The surface area is the sum of areas of all the faces of the three-dimensional figure.
Plane 2D figures represent the area. Example: circles, rectangles, and triangles.	Solid 3D figures represent the surface area. Examples: cylinder, prisms, pyramids, and cones.
When we have to calculate an area all we have to do is concentrate on the area of one figure.	In the surface area, when we have to calculate surface area, we have to work out the area of all the faces.
Example: The formula of area for the rectangle is – length x width.	Example: The formula to calculate the surface area for a cuboid is – SA = 2lw+2lh+2hw.

Formulas for Area Related to 2D Shapes

Name of Geometric Shapes	Area Formula	Variables
Rectangle	Area = l × w	l = length w = width
Square	Area = a2	a = sides of the square
Triangle	Area = ½ x b x h	b = base h = height
Trapezoid	Area = 1/2 (a + b)h	a =base 1 b = base 2 h = vertical height
Parallelogram	Area = b × h	a = side b=base h=vertical height
Rhombus	Area = a x 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

Formulas for Lateral/ Curved Surface Area and Total Surface Area Related to 3d Shapes(Solid Shapes)

S.No	Name	Abbreviations used	Lateral /Curved Surface Area	Total Surface Area
1.	Cuboid	h = height, l = length b=breadth	2h(l+b)	(l × b) + (l × b) + (l × h) + (l × h) + (b × h) + (b × h).
2.	Cube	a = length of the sides	4a2	6a2
3.	Right Prism	..	Perimeter of Base × Height	Lateral Surface Area + 2(Area of One End)
4.	Right Circular Cylinder	r= radius h=height	2 (π × r × h)	2πr (r + h)
5.	Right pyramid	..	½ (Perimeter of Base × Slant Height)	Lateral Surface Area + Area of the Base
6.	Right Circular Cone	r = radius l = length	πrl	πr (l + r)
7.	Sphere	r = radius	4πr2	4πr2
8.	Hemisphere	r = radius	2πr2	3πr2

Solved Examples

Find the total surface area of a cylindrical tin of radius 17 cm and height 4 cm.

Solution:

Given that: r = 17cm and h = 4cm

We have total surface area formula of a cylinder as (TSA) = 2πr (h + r) sq.units

Therefore TSA = 2 x 22/7 x 17(17 + 4)

= 2 x 22/7 x 17 x 21

= 2444cm2

Therefore, the total surface area of a cylindrical tin is 2444cm2.

Conclusion

This is all about the definition and explanation of the differences between area and surface area. Understand the logic and concept by referring to examples as much as possible. Find out how the area of 2D shapes is determined to understand the concept well.

FAQs on Difference Between Area and Surface Area for JEE Main 2024

1. What is the Difference Between Area and Volume?

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.

2. What are 2D shapes?

The two-dimensional shapes (2D shapes), also known as flat shapes, refer to those shapes which have two dimensions only. It has a length and a breadth and does not have any thickness. The two different measures that are used for measuring the flat shapes are the area and the perimeter. The shape that can be easily drawn on a piece of paper is a two-dimensional shape. Some examples of 2D shapes are the square, the rectangle, the circle, the triangle, etc.

3. What are 3D shapes?

The three-dimensional shapes (3D shapes)also known as solid shapes, refer to those shapes which have three dimensions only, such as length, breadth, and thickness. The distinct measures used to define a three-dimensional shape are the volume and the surface area. The three-dimensional shapes are obtained from The rotation of the two-dimensional shapes to help get the three dimensional shapes. If you want to calculate the surface area of solid shapes, it can be calculated from the area of 2D shapes.