Calculating the circumference of a circle given the area

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Ngày cập nhật gần nhất: 15/4/2026

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Calculating the circumference of a circle given the area

1. Method to calculate the circumference of a circle given the area

2. Expanded Knowledge: Differentiating between a circle and a disc

Students are familiar with calculating the area of a circle when the circumference is known. But how do they calculate the circumference of a circle when the area is given? Follow our article to understand more about solving this exercise.

The circumference of a circle is the boundary of the circle, denoted as C, while the area of a circle is everything that can be visualized within the shape, denoted as A or S; the unit of area is square meters (symbol: m²). We have encountered many problems related to the circumference and area of a circle, but when it comes to calculating the circumference of a circle given the area, what knowledge do we need to apply to solve the problem quickly and accurately?

Calculating the circumference of a circle given the area

1. Method to calculate the circumference of a circle given the area

To solve the problem of finding the circumference of a circle given the area, follow these two steps:

Application Exercise : Given that the area of the circle is 28.26 (cm²), calculate the circumference of the circle.

Method 1:
Applying the formula A = π .r²
We have: 28.26 = 3.14 x r²
=> r² = 28.26 : 3.14
=> r² = 9
=> r = 3 (cm)

Applying the formula: C = r x 2π => The circumference of the circle is: 3 x 2 x 3.14 = 18.84 (cm).
Answer: 18.84cm.

2. Expanded Knowledge: Differentiating between a circle and a disc

- A disc is the area inside a circle. The center and radius of the disc are the center and radius of the circle surrounding it.
- A circle is the boundary around the disc, it is a set of all points on a plane, equidistant from a given point (center) by a certain distance (radius).

In this article, we have guided students on how to complete exercises on calculating the circumference of a circle given the area. Students can apply those hints to solve exercises on calculating the circumference or area of a circle independently. Parents of students can also refer to this article to guide their children in studying at home more easily.

Furthermore, students can also refer to other types of exercises on calculating the circumference of a circle given specific conditions, such as exercises on calculating the circumference of a circle given the radius r. This is also a common type of exercise on circles that students need to master.

Frequently Asked Questions

What is the process for calculating the circumference of a circle given the area?

To calculate the circumference of a circle when the area is known, first use the formula A = πr² to find the radius. Then apply C = 2πr to determine the circumference.

How do you differentiate between a circle and a disc in geometry?

A circle refers to the boundary or perimeter, while a disc is the area contained within that boundary. Both share the same center and radius, but they represent different geometric concepts.

Can students calculate the circumference if they only know the area of the circle?

Yes, students can calculate the circumference of a circle if they know the area. By applying the formulas for area and circumference, they can determine the radius first, then find the circumference.

What example illustrates calculating the circumference from a given area of a circle?

For an area of 28.26 cm², first solve for the radius using A = πr², which gives r = 3 cm. Then use C = 2πr to find the circumference, resulting in 18.84 cm.

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