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Maths > Circles > Circumference of a Circle
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Circumference of a Circle

The circumference of circle or the perimeter of a circle refers to the measurement of the border across any 2D circular shape including the circle.  However, the area of the circle describes the area engaged by it. Let us more about circumference of circle here in detail.

Definition

In case we are opening a circle and making a straight line out of it, then its length will be its circumference. Thus, we usually measure it in unit ‘cm’ or’.

Further, whenever we apply the formula for calculating the circumference of the circle, at that time, the radius of the circle is taken into account. Therefore, we are required to know the value of the radius or the diameter for evaluating the perimeter of the circle.

Formula

The Circumference or Perimeter of a circle is: 2πR. Here, ‘r’ refers to the radius of the circle. Moreover, ‘π’ is the mathematical constant having an approximate value of about 3.14. Again, ‘π’ is a special mathematical constant here, it is the ratio in a circle, of circumference to diameter, where ‘C’ = ‘πD’, ‘C’ is the circumference, ‘D’ is the diameter, for instance: If the radius of the circle is 4 cm then find out the circumference of a circle: Given:

Radius ‘r’ = 4 cm

Circumference ‘C’ = 2πr

= 2 x 3.14 x 4

= 25.12 cm.

Formula for the Area of a Circle

The area enclosed by the circle itself or the space covered by it is known as the area of a circle. Formula to find out the area of a circle is ‘A = πr2’. Where ‘r’ is the radius. This formula is valid for all the circles having different radii.

Perimeter of a Semi-Circle

The semi-circle is made after the division of the circle into 2 similar parts. Hence, the perimeter of the semi-circle also turn into a half:

Perimeter of s semi-circle = ‘2πr/2 = πr’.

Area of a Semi-Circle

The area of a semi-circle is the section occupied by a semi-circle in a two-dimensional plane. Thus, the area of the semi-circle is equivalent to the half area of a circle, which have equal radii.

So, Area of a semi-circle = ‘πr2/2’.

Radius of a Circle

Radius refers to the distance from the middle to the outer line of the circle. Further, it is the most essential quantity of the circle. Double the radius of a circle is known as the diameter of a circle.

Methods to Find-Out the Circumference:

1st Method: We aren’t able to physically measure the length of the circle with the help of a scale or a ruler because it is a curved surface. However, we can do this for polygons like squares, rectangles, and triangles. Thus, we can measure a circle’s circumference with a thread. We have to trace the path of the circle with the thread and mark all those points over the thread. The length is measurable with the use of a normal ruler.

2nd Method: In this method, we have to calculate the circumference of the circle. Further, the calculation is important so that we can get an accurate value. For this method, we must be knowing the radius of the circle. In other words, the radius is the length from the middle of the circle to its outer line.

Solved Example for You

Question 1: Find out the radius of a circle that has ‘C’ = 50 cm.

Solution:

Circumference = ‘C’ = 50 cm

According to the formula; ‘C’ = ‘2πr‘

This implies, 50 = 2πr

50/2 = 2πr/2

25 = πr

Or we can say ‘r’ = 25/π

Therefore, the radius of the circle will be 25/π cm.

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