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128 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Sphere
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:
Mistake 1
Confusing radius with diameter.
A basic mistake is using the diameter instead of the radius.
Remember that the diameter is twice the radius, so ensure you use the correct value for the radius in calculations.
Mistake 2
Incorrectly squaring the radius.
A simple yet common mistake is failing to square the radius correctly in the formula.
Double-check your calculations to avoid this error.
Mistake 3
Not mentioning the units with the numerical value.
It's important to mention the unit with the answer, even if the question doesn't specify the unit.
It's preferable to write “square units” for clarity.
Mistake 5
Misinterpreting the formula for total surface area.
The formula for the lateral surface area of a sphere is specific and should not be confused with formulas for other shapes, such as the cone.
Solved examples on Lateral Surface Area of a Sphere
Problem 1
What is the lateral area of a sphere with a radius of 5 cm?
314 cm²
Explanation
Given: Radius r = 5 cm,
LSA = 4πr² = 4×3.14×5² = 314 cm²
Problem 2
If the lateral surface area of a sphere is 113.04 cmยฒ, find the radius.
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
Problem 3
Calculate the lateral surface area of a sphere with a diameter of 10 cm.
314 cm²
Explanation
Given: Diameter = 10 cm, hence Radius r = 5 cm
LSA = 4πr² = 4×3.14×5² = 314 cm²
Problem 4
Evaluate the radius of a sphere if its lateral surface area is 201.06 square units. (Use ฯ = 22/7)
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
Problem 5
The lateral surface area of a sphere is 452.16 cmยฒ. Find the radius.
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
FAQโs on Lateral Surface Area
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area.
3.Is the lateral surface area and total surface area the same for a sphere?
4.What happens when the radius of a sphere is doubled?
5.Why is the formula for a sphere's surface area different from that of a cone?
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.
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.
Fun Fact
: She has songs for each table which helps her to remember the tables
