Surface Area Formulas (original) (raw)

Last Updated : 23 Jul, 2025

Surface area refers to the total area that the surface of a three-dimensional object occupies. It is a measure of how much-exposed area the object has. It’s used in various fields like engineering, architecture, and design to determine the material needed for constructing or covering objects.

The method for calculating surface area varies depending on the shape of the object. Here, we will explore the different surface area formulas used to determine the total area of the outer surfaces of three-dimensional geometric shapes.

Learning surface area formulas helps in quickly solving the questions appearing on exams as well as practical applications like calculating material requirements, understanding scientific processes, and addressing engineering problems.

Types of Surface Area

Surface Area is only calculated for 3-D figures. We can have two types of Surface Areas:

**Lateral/Curved Surface Area

• It refers to the area of all the sides of a three-dimensional object, excluding the base(s).
• It specifically focuses on the "sides" or "walls" of the object.

**Total Surface Area

• **It refers to the sum of the areas of all the outer surfaces (including both the lateral surface and the bases).
• It covers the entire area of an object.

The table below highlights the key differences, formulas, and applications of Lateral Surface Area (LSA) and Total Surface Area (TSA):

Formulas for Surface Area

Surface area formulas are given for the total surface area (TSA) and the lateral surface area (LSA). The total surface area includes the area of all surfaces of the object (base + sides), while the lateral surface area includes only the area of the sides, excluding the base.

There are various surface area formulas, and some of the key surface areas for important geometric figures are listed in the table below:

Surface Area Formulas

**Try the Quiz - [**Surface Area and Volume Quiz**]

Surface Area Formulas List

The following table contains the surface area formulas of different shapes

Shape	Figure	Lateral Surface Area (LSA)	Total Surface Area (TSA)
Cube		4a2	6a2
Cuboid		2h(l+b)	2(lb + lh + bh)
Cylinder		2πrh	2πr(r + h)
Cone		πrl	πr(l + r)
Sphere		4πr2	4πr2
Hemisphere		2πr2	3πr2
Pyramid		1/2 × (Base Perimeter) × (Slant Height)	LSA + Area of Base
Prism		(Base Perimeter) × (Height)	LSA + 2(Area of Base)

**Surface Area of Different Shapes in Detail

Below are the formulas, along with the definitions and figures, for the Lateral Surface Area (LSA) and Total Surface Area (TSA) of various 3D geometrical figures.

**Surface Area Formula of Cube

A cube is a six-faced 3D shape in which all the faces are equal. A cube is a three-dimensional shape with several key characteristics:

Formulas for the Surface Area of Cube a are given by:

• **Lateral Surface Area (LSA) of Cube = 4a 2
• **Total Surface Area (TSA) of Cube = 6a 2

Where **a is the Side of a Cube.

To learn more about the formulas related to a **Cube, here are the key ones:

• Volume of a Cube
• Surface Area of Cube

**Surface Area Formula of Cuboid

A Cuboid is a 3D figure in which opposite faces are equal. A cuboid, also known as a rectangular prism, is a 3D geometric shape very similar to a cube, but with some key differences:

Formulas for the Surface Area are given by:

• **Lateral Surface Area (LSA) of Cuboid = 2 × (hl + bh)
• **Total Surface Area (TSA) of Cuboid = 2 × (hl + bh + bh)

Where:

• **l is the length of the Cuboid
• **b is the Breadth of Cuboid
• **h is the Height of the Cuboid

To learn more about the formulas related to a **Cuboid, here are the key ones:

• Volume of Cuboid
• Surface Area of a Cuboid

**Surface Area Formula of a Sphere

The sphere is a 3D figure that is similar to a real-life ball. A sphere is a three-dimensional, perfectly round object with several key characteristics:

The formula for the Surface Area of a Sphere is:

**Surface Area of Sphere = 4πr 2

Where **r is the Radius of the Sphere.

To learn more about the formulas related to a **Sphere, here are the key ones:

• Surface Area of a Sphere
• Volume of a Sphere

**Surface Area Formula of a Hemisphere

The hemisphere is a 3D figure that is half of the Sphere. It is created by slicing it through its center with a flat plane.

The formula for the Area of a Hemisphere formula is:

• **Curved Surface Area (CSA) of Hemisphere = 2πr 2
• **Total Surface Area (TSA) of Hemisphere = 3πr 2

Where **r is the Radius of the Sphere.

To learn more about the formulas related to a **Hemi-sphere, here are the key ones:

• Area of a Hemisphere
• Volume of Hemisphere

**Surface Area Formula of a Cylinder

A cylinder is a 3D figure with two circular bases and a curved surface.

The formula for the Area of a Cylinder is:

• **Curved Surface Area (CSA) of Cylinder = 2πrh
• **Total Surface Area (TSA) of Cylinder = 2πr 2 + 2πrh = 2πr(r+h)

Where:

• **r is the Radius of the base of the Cylinder
• **H is the Height of Cylinder

To learn more about the formulas related to a **Cylinder, here are the key ones:

• Area of a Cylinder
• Volume of a Cylinder

Surface Area Formula of a Cone

A cone is a 3D geometric shape with a circular base and a pointed edge at the top called the apex. A cone has one face and a vertex.

The Formula for the Surface Area of the Cone is:

**Curved Surface Area (CSA) of Cone = πrl

**Total Surface Area (TSA) of Cone = πr(r + l)

Where:

• **r is the Radius of the Base of the Cone
• **l is the Slant Height of the Cone

To learn more about the formulas related to a **Cone, here are the key ones:

• Surface Area of Cone
• Volume of a Cone

**Surface Area Formula of Pyramid

A pyramid is a 3D figure having triangular faces and a triangular base. It is a three-dimensional polyhedron with a polygonal base and triangular sides that meet at a common point called the apex.

The formula for the Surface Area of a Pyramid is:

• **Lateral Surface Area (LSA) of Pyramid = 1/2 × (Perimeter of Base) × Height
• **Total Surface Area (TSA) of Pyramid = [1/2 × (Perimeter of Base) × Height] + Area of Base

To learn more about the formulas related to a **Pyramid, here are the key ones:

• Surface Area of a Pyramid
• Volume of a Pyramid

Solved Examples of Surface Area Formulas

**Example 1: Find the lateral surface of a Sphere with a radius of 4 cm.
**Solution:

Given,
Radius of Sphere (r) = 4 cm

Formula of Lateral Surface Area of Sphere = 4πr2
LSA = 4 × 3.14 × r × r = 4 × 3.14 × 4 × 4
LSA = 200.96 cm2

**Example 2: Find the lateral surface of a Hemi-Sphere with a radius of 6 cm.
**Solution:

Given,
Radius of Hemisphere (r) = 6 cm

Formula of Lateral Surface Area of Hemi-Sphere = 2πr2
LSA = 2 × 3.14× r × r = 2 × 3.14 × 6 × 6
LSA = 226.08 cm2

**Example 3: Find the Total surface of a Cube with a side of 10 m.
**Solution:

Given,
Side of Cube (a) = 10 cm

Formula of Total Surface Area of Cube = 6a2
TSA = 6 × a × a = 6 × 10 × 10
TSA = 600 m2

**Related Articles:

• Volume Formulas
• Volume of Cube
• Volume of Cylinder
• Volume of Cuboid