Circumference of a Circle

Circumference of the circle is the measurement of the boundary across any two-dimensional circular shape including circle.  The concept of the perimeter of a circle is covered here along with its definition, formula and method to know the same by using formula and physical method along with some solved examples. Finding area of a circle also requires the same radius as for finding the circumference.

Circle

What is the Circumference of Circle?

The circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface. It follows the same principle behind finding the perimeter of any polygon which is why calculating the circumference of a circle which is also known as the perimeter of a circle.

A circle is defined as a shape with all the points are equidistant from a point at the centre. The circle depicted below has its centre lies at point A.

The value of pi is approximately 3.1415926535897… and we use a Greek letter π (pronounced as Pi) to describe this number. The value π is a non-terminating value.

For circle A (as given above), the circumference and the diameter will be-

Circumference of a Circle

In other words, the distance surrounding a circle is known as the circumference of the circle. The diameter is the distance across a circle through the centre and it touches the two points of the circle perimeter. π shows the ratio of the perimeter of a circle to the diameter. Therefore, when you divide the circumference by the diameter for any circle, you obtain a value close enough to π. This relationship can be explained by the formula mentioned below.

C/d = π

Where C indicates circumference and d indicates diameter. A different way to put up this formula is C = π × d. This formula is mostly used when the diameter is mentioned and the perimeter of a circle needs to be calculated.

Circumference Formula of a Circle

The Circumference (or) perimeter of a circle = 2πR

where,

R is the radius of the circle

π is the mathematical constant with an approximate (up to two decimal points) value of 3.14

Again,

Pi (π) is a special mathematical constant, it is the ratio of circumference to diameter of any circle.

where C = π D

C is the circumference of the circle

D is the diameter of the circle

Area of a Circle

Area of any circle is the region enclosed by the circle itself or the space covered by the circle. The formula to find the area of the circle is;

A = πr2

Where r is the radius of the circle. This formula is applicable to all the circles with different radii.

Radius of a Circle

The distance from the centre to the outer line of the circle is called a radius. It is the most important quantity of the circle based on which formulas for area and circumference of the circle are derived. Twice the radius of a circle is called as the diameter of the circle. The diameter cuts the circle into two equal parts, which is called as a semi-circle.

Methods to Calculate the Circumference of a Circle

Method 1: Since it is a curved surface, we can’t physically measure the length of a circle using a scale or ruler. But this can be done for polygons like squares, triangles and rectangles. Instead, we can measure the circumference of a circle using a thread. Trace the path of the circle using the thread and mark the points on the thread. This length can be measured using a normal ruler.

Method 2: An accurate way of knowing the circumference of a circle is to calculate it. For this, the radius of the circle has to be known. The radius of a circle is the distance from the centre of the circle and any point on the circle itself. The figure below shows a circle with radius R and centre O. The diameter is twice the radius of the circle.

Circumference of a Circle Method

 

Perimeter of a Circle Example Problems

Question 1:

What is the circumference of the circle with diameter 4 cm?

Solution:

Since the diameter is known to us, we can calculate the radius of the circle,

Therefore, Circumference of the Circle = 2 x 3.14 x 2 = 12.56 cm.

Question 2: Find the radius of the circle having C =  50 cm.

Solution: 

Circumference = 50 cm

As per formula,  C = 2 π  r

This implies, 50 = 2 π  r

50/2 = 2 π  r/2

25 = π  r

or r =  25/π 

Therefore, the radius of the circle is 25/π  cm.

Circumference of a Circle Questions

  1. Calculate the perimeter of a circle whose diameter is 8 cm.
  2. What will be the diameter of a circle if its C =  10 cm?
  3. If C =  12 cm, what will be its radius?
  4. What is the circumference of a 16-inch circle?
  5. What is the circumference of a 6 mm circle?

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