Lateral Surface Area of a Sphere
2026-02-28 09:08 Diff
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Last updated on December 11, 2025

A sphere is a perfectly symmetrical three-dimensional shape, like a ball, consisting only of a curved surface. Unlike a cone, it does not have a base. The entire outer surface of the sphere is its lateral surface. Let's take an example of a basketball. The entire outer part of the basketball represents the lateral surface area of the sphere.

What is the Lateral Surface Area of a Sphere?

For a sphere, the lateral surface area is simply the total surface area, as it consists only of a curved surface with no bases.

It is represented by the formula that calculates the entire outer surface of the sphere.

Formula for Lateral Surface Area of a Sphere

The lateral surface area of a sphere can be calculated using the radius “r” of the sphere.

The formula for the lateral surface area is given by Area = 4πr². This formula arises from the geometry of the sphere as a perfectly rounded shape.

How to Find Lateral Surface Area of a Sphere

In order to find the Lateral Surface Area of a Sphere, the following steps must be followed.

Step 1: Take note of the given radius.

Step 2: Ensure that the measurement is in the correct unit before the calculation.

Step 3: Use the equation, Area = 4πr², to find the LSA of the sphere.

Step 4: Provide the calculated answer in square units.

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Common mistakes and how to avoid them in the Lateral Surface Area of a Sphere.

There are a few typical mistakes people make while calculating the lateral surface area of a sphere.

Some of them are listed below:

Problem 1

What is the lateral area of a sphere with a radius of 5 cm?

Okay, lets begin

314 cm²

Explanation

Given: Radius r = 5 cm,

LSA = 4πr² = 4×3.14×5² = 314 cm²

Well explained 👍

Problem 2

If the lateral surface area of a sphere is 113.04 cm², find the radius.

Okay, lets begin

3 cm

Explanation

Given: LSA = 113.04 cm²

Using the formula, LSA = 4πr²

113.04 = 4×3.14×r²

r² = 113.04/12.56

r² = 9

r = 3 cm

Well explained 👍

Problem 3

Calculate the lateral surface area of a sphere with a diameter of 10 cm.

Okay, lets begin

314 cm²

Explanation

Given: Diameter = 10 cm, hence Radius r = 5 cm

LSA = 4πr² = 4×3.14×5² = 314 cm²

Well explained 👍

Problem 4

Evaluate the radius of a sphere if its lateral surface area is 201.06 square units. (Use π = 22/7)

Okay, lets begin

4 units

Explanation

Given: LSA = 201.06 square units

Using the formula, LSA = 4πr²

201.06 = 4×22/7×r²

r² = 201.06×7/88

r² = 16

r = 4 units

Well explained 👍

Problem 5

The lateral surface area of a sphere is 452.16 cm². Find the radius.

Okay, lets begin

6 cm

Explanation

Given: LSA = 452.16 cm²,

Using the formula, LSA = 4πr²

452.16 = 4×3.14×r²

r² = 452.16/12.56

r² = 36

r = 6 cm

Well explained 👍

FAQ’s on Lateral Surface Area

1.What is Lateral Surface Area?

The lateral surface area of a sphere is the total surface area of its curved surface, as the sphere is entirely composed of this surface.

2.How to calculate the lateral surface area.

The Lateral Surface Area of a sphere can be calculated using the formula: Area = 4πr²

3.Is the lateral surface area and total surface area the same for a sphere?

Yes, for a sphere, the lateral surface area is the same as the total surface area because it is only composed of a curved surface.

4.What happens when the radius of a sphere is doubled?

When the radius of a sphere is doubled, its lateral surface area becomes four times larger because the area is proportional to the square of the radius.

5.Why is the formula for a sphere's surface area different from that of a cone?

The formula is different because a sphere is a perfectly symmetrical 3D shape with no bases, unlike a cone, which has both a base and a curved surface.

Important Glossary for Lateral Surface Area

  • Radius: The distance from the center of the sphere to any point on its surface.
  • Diameter: The longest distance across the sphere, passing through the center, equal to twice the radius.
  • π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles and spheres.
  • Sphere: A three-dimensional shape that is perfectly round, like a ball, consisting only of a curved surface.
  • Lateral Surface Area: The total area of the curved surface of a three-dimensional shape, such as a sphere.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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