Surface Area of Circle
2026-02-28 01:27 Diff

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Last updated on September 4, 2025

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.

Problem 1

Given r = 7 cm. Use the formula: Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm²

Okay, lets begin

Find the circumference of a circle with a radius of 5 cm.

Explanation

Circumference = 31.4 cm

Well explained 👍

Problem 2

Use the formula: Circumference = 2πr = 2 × 3.14 × 5 = 31.4 cm

Okay, lets begin

A circle has a diameter of 12 cm. Find its area.

Explanation

Area = 113.04 cm²

Well explained 👍

Problem 3

Find the radius using: r = Diameter/2 = 12/2 = 6 cm Use the Area formula: Area = πr² = 3.14 × 6 × 6 = 3.14 × 36 = 113.04 cm²

Okay, lets begin

Find the area of a circle with a diameter of 14 cm.

Explanation

Area = 154 cm²

Well explained 👍

Problem 4

Find the radius: r = Diameter/2 = 14/2 = 7 cm Use the formula: Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm²

Okay, lets begin

The circumference of a circle is 66 cm. Find the radius.

Explanation

Radius = 10.5 cm

Well explained 👍

It is the total area that is enclosed by the circle's boundary.

1.What is the formula for the area of a circle?

The formula for the area of a circle is πr², where r is the radius.

2.What is the difference between the diameter and the radius?

The diameter is twice the length of the radius. The diameter is the longest line that can fit inside the circle, passing through the center.

3.How do you find the circumference of a circle?

The circumference is found using the formula 2πr, where r is the radius.

4.What unit is the surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

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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.

Fun Fact

: She has songs for each table which helps her to remember the tables