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174 LearnersLast updated on September 4, 2025
Surface Area of Circle
A circle is a 2-dimensional shape that is perfectly round and has no corners. The surface area of a circle refers to the area enclosed within its circumference. In this article, we will learn about the surface area of a circle.
What is the Surface Area of a Circle?
The surface area of a circle is the total area enclosed by its boundary or circumference. It is measured in square units.
A circle is a simple closed shape formed by all points in a plane that are at a given distance from a fixed point, the center.
The surface area of a circle is also known as the area of the circle and is calculated using the radius, which is the distance from the center to any point on the circle.
Surface Area of a Circle Formula
The surface area of a circle is calculated using its radius. The formula to find the area of a circle is: Area = πr² square units Here, r is the radius of the circle.
Calculating Surface Area of a Circle
To find the surface area of a circle, you only need to know its radius.
Using the formula: Area = πr² where r is the radius of the circle, you can determine the area.
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Circumference of a Circle
The circumference of a circle is the distance around it.It is calculated by using the formula:
Circumference = 2πr where r is the radius of the circle.
Diameter and Radius Relationship
The diameter of a circle is twice the radius. The formula for diameter is: Diameter = 2r
This relationship is important for calculating both the area and the circumference of a circle.
Confusion between Circumference and Area
Students sometimes confuse the formula for circumference with the formula for area. Remember, circumference is 2πr, while area is πr².
Mistake 1
Using Diameter Instead of Radius
Some students mistakenly use the diameter instead of the radius when finding the area. Always use the radius in the formula for area.
Mistake 3
Forgetting to Square the Radius
Students often forget to square the radius in the area formula. Always remember that the formula is πr², not just πr.
Mistake 4
Assuming Diameter and Radius Are the Same
Some students mistakenly believe that diameter and radius are the same, but the diameter is twice the radius. Ensure you use the correct measurement in formulas.
Mistake 5
Solved Examples of Surface Area of Circle
Find the area of a circle with a radius of 7 cm.
Area = 154 cmยฒ
Problem 1
Given r = 7 cm. Use the formula: Area = ฯrยฒ = (22/7) ร 7 ร 7 = 22 ร 7 = 154 cmยฒ
Find the circumference of a circle with a radius of 5 cm.
Explanation
Circumference = 31.4 cm
Problem 2
Use the formula: Circumference = 2ฯr = 2 ร 3.14 ร 5 = 31.4 cm
A circle has a diameter of 12 cm. Find its area.
Explanation
Area = 113.04 cm²
Problem 3
Find the radius using: r = Diameter/2 = 12/2 = 6 cm Use the Area formula: Area = ฯrยฒ = 3.14 ร 6 ร 6 = 3.14 ร 36 = 113.04 cmยฒ
Find the area of a circle with a diameter of 14 cm.
Explanation
Area = 154 cm²
Problem 4
Find the radius: r = Diameter/2 = 14/2 = 7 cm Use the formula: Area = ฯrยฒ = (22/7) ร 7 ร 7 = 22 ร 7 = 154 cmยฒ
The circumference of a circle is 66 cm. Find the radius.
Explanation
Radius = 10.5 cm
It is the total area that is enclosed by the circle's boundary.
1.What is the formula for the area of a circle?
2.What is the difference between the diameter and the radius?
3.How do you find the circumference of a circle?
4.What unit is the surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Circle
Students often make mistakes while calculating the surface area of a circle, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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
