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# Circumference of Circle Formula, Meaning & Definition

## Circumference of Circle Meaning & Definition

The circumference is the outer boundary of any shape and circumference is also known as the perimeter. Every shape has a circumference, the outer periphery that surrounds the shape. We have many geometrical shapes in maths such as triangle, square, circle. These all shapes are called 2-dimensional shapes. We have 3-dimensional shapes too which are cone, sphere, cylinder, cube. These all shapes are called 3-dimensional shapes. In this article, we will discuss the circumference of 2-dimensional shapes. To get notification of related topics, do bookmark this page, here we post some interesting and complex concepts in laymen’s language so that students can understand better.

## Circumference of Circle Formula

The circumference of a circle is the length of its periphery.  Let’s take a look at the components that make up circumference. The three most important elements of a circle are :

Center: The center is located equidistance from every other point on the circle.

Diameter: The diameter of a circle is the distance from the center to the circumference.

Radius: The radius of a circle is the distance between the circle’s center and any point along its perimeter.

 Circumference Formula of Circle(c) = 2πr

Where r is the radius of the circle and c is the circumference of the circle. Suppose the radius of the circle is not given the how the circumference of a circle will be calculated?

We know that the radius of the circle is half of the diameter of the circle. If the diameter of a circle is given then also we can find the circumference by putting r = d/2 in the same formula given above.

Circumference Formula of Circle(c) = 2πr

Substitute radius of circle r = d/2

Circumference Formula of Circle(c) = 2π* (d/2)

 Circumference Formula of Circle(c) =πd

## Circumference of Semicircle Formula

Semicircle is the half of the circle i.e. it is formed when we divide the circle into two equal parts. If we are dividing the circle into equal parts then the circumference of the circle will also be divided equally. Let us know the Circumference Formula of Semicircle.

 Circumference Formula of Semicircle =  (πr+2r)

Here the r is the radius of the circle.

## Circumference of Circle Formula: Solved Examples

Example 1:  What is the circumference of the circle with a diameter 6 cm?

Solution: In the question, we have given the diameter of the circle, we can find the radius of the circle by putting r = d/2 in the formula of Circumference of Circle.

Circumference Formula of Circle(c) = 2πr

Circumference Formula of Circle(c) = πd

C = (22/7)6

Therefore, Circumference of the Circle(C) = 18.85 cm

Example 2: Find the radius of the circle having C =  100 cm.

Solution: In the question, we have given the circumference of the circle and we have to calculate the radius of the circle. We will put this value of circumference in the formula of the circumference of the circle.

Circumference Formula of Circle(c) = 2πr

100 = 2 π  r

50 = π  r

Therefore, 50 = 22/7* r

The radius of the circle is = 15.90cm

Therefore, the radius of the circle is 15.90cm

Example 3: Find the perimeter of a circle whose radius is 9 cm?

Solution: In this question, we have given the radius = 9 cm. And we have to find the circumference of the circle. We have studied the circumference formula above. We will put the value of radius in the circumference formula to calculate the circumference of the circle.

We know that the circumference of a circle = 2πr

Now, substitute the radius value in the circumference formula

C = (2)*(22/7)*(9)  cm

C = 56.57cm

Therefore, the circumference of the circle is 56.57 cm.

Example 4: Calculate the circumference of the circle in terms of π, whose diameter is 12m.

Solution: In this question, we have given the diameter of the circle which is 12m and we have to calculate the circumference of the circle in terms of π.

We know that, the radius of circle = d/2

Circumference of circle = 2πr = 2*π*6

C = 2π(6) = 12π m.

Therefore, the perimeter of the circle in terms of π, whose diameter is 12 cm is 12π m.

Example 5: Find the perimeter of a circle whose radius is 13 cm?

Solution: In this question, we have given the radius = 13 cm. And we have to find the circumference of the circle. We have studied the circumference formula above. We will put the value of radius in the circumference formula to calculate the circumference of the circle.

We know that the circumference of a circle = 2πr

Now, substitute the radius value in the circumference formula

C = (2)*(22/7)*(13)  cm

C = 81.71 cm

Therefore, the circumference of the circle is 81.71 cm.

Example 6: Calculate the circumference of the circle in terms of π, whose diameter is 20m.

Solution: In this question, we have given the diameter of the circle which is 20m and we have to calculate the circumference of the circle in terms of π.

We know that, the radius of circle = d/2 = 20/2 =10

Circumference of circle = 2πr = 2*π*10

C = 2π(10) = 20π m.

Therefore, the perimeter of the circle in terms of π, whose diameter is 20 cm is 20π m.

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## FAQs on Circumference of Circle Formula

Q.What is the circumference of the circle?

The circumference is the outer boundary of any shape and circumference is also known as the perimeter. So the circumference is the outer periphery of the circle and is also called the perimeter of the circle.

Q. What is the formula for the circumference of a circle?

The formula for the circumference of a circle is 2πr.

circumference of a circle = 2πr

Q. What is the formula of the circumference of a semicircle?

The formula of the circumference of a semicircle is πr+2r.

Q. What is the circumference of a semicircle?

The semicircle is formed when we divide the circle into equal parts. Hence, the circumference of the semicircle will be half of the circumference of the circle.

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## FAQs

### Q. What is the circumference of the circle?

The circumference is the outer boundary of any shape and circumference is also known as the perimeter. So the circumference is the outer periphery of the circle and is also called the perimeter of the circle.

### Q. What is the formula of the circumference of a circle?

The formula for the circumference of a circle is 2πr.

circumference of a circle = 2πr

### Q. What is the formula of the circumference of a semicircle?

The formula of the circumference of a semicircle is πr+2r.

### Q. What is the circumference of a semicircle?

The semicircle is formed when we divide the circle into equal parts. Hence, the circumference of the semicircle will be half of the circumference of the circle.

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