Circumference of a circle

Circumference of a circle
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The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park, or a circular table to be bordered requires this metric of the circumference of a circle. The circumference is a linear value and its units are the same as the units of length.

A Circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center. The two important metrics of a circle is the area of a circle and the circumference of a circle. Here we shall aim at understanding the formula and calculation of the circumference of a circle.

Table of Contents

What is Circumference of a Circle

The circumference of a circle is its boundary or the length of the complete arc of a circle. Let us understand this concept using an example. Consider a circular park as shown below.

Understanding Circumference of a Circle

If a boy starts running from point 'A' and reaches the same point after taking one complete round of the park, a distance is covered by him. This distance or boundary is called the circumference of the park which is in the shape of a circle. The circumference is the Length of the Boundary. 

Circumference of a Circle Definition

The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.

Formula for the Circumference of a Circle

The circumference of a circle can be calculated using the radius  'r' of the circle and the value of 'pi'. Circumference of a circle = 2πr. While using this formula, if we do not have the value of the radius, we can find it using the diameter. That is, if the diameter is known, it can be divided by 2 to obtain the value of the radius because Diameter of a circle = 2 × r. Another way to calculate the circumference of a circle is by using the formula: Circumference = π × Diameter. If we need to calculate the radius or diameter, when the circumference of a circle is given, we use the formula: Radius = Circumference/2π 

Calculation of the Circumference of a Circle 

Although the circumference of a circle is its length, it cannot be calculated with the help of a ruler (scale) like it is usually done for other polygons. This is because a circle is a curved figure. Therefore, to calculate the circumference of a circle, we apply a formula that uses the radius or the diameter of the circle and the value of Pi (π).

Circumference of a Circle

Radius: Radius is the distance from the center of a circle to the boundary of the circle.

Diameter: Diameter is a straight line passing through the center that connects two points on the boundary of the circle.

Pi: Pi is a special mathematical constant with a value approximated to 3.14159 or π =  22/7. The value of π =  22/7 is used in various formulas. It is the ratio of circumference to diameter, where C = πD


Important Notes

  •  π(Pi) is a mathematical constant which is the ratio of the circumference of a circle to its diameter. It is approximated to π =  22/7or 3.14
  • If the radius of a circle is extended further and touches the boundary of the circle, it becomes the diameter of a circle. Therefore, Diameter = 2 × Radius
  • The circumference is the distance around a circle or the length of a circle
  • We can find the circumference of a circle using the radius or diameter
  • Circumference = π× Diameter; Circumference = 2πr.

Circumference of a Circle Related Topics

Given below is the list of topics that are closely connected to the Circumference of a Circle. These topics will also give you a glimpse of how such concepts are covered in Cuemath. 


FAQs on Circumference of a Circle

What is the Circumference of a Circle?

The circumference of a circle is its boundary or the length of the complete arc of a circle. The circumference of the circle is the product of π a constant and d the diameter of the circle. The circumference of a circle is a linear quantity that has the same units of length. 

How do you Calculate the Circumference of a Circle?

The circumference of a circle is calculated with the help of a formula that needs the value of the radius and Pi. Circumference of a circle = 2πr 

How do you Calculate the Diameter From the Circumference of a Circle?

If we need to calculate the radius or diameter when the circumference of a circle is given, we use the formula: Circumference = π × Diameter or we have Diameter = Circumference π.

How do you Find the Circumference of the Circle With the Area?

The circumference of a circle can be easily found from the area of the circle. From the area of the circle, we can compute the radius of the circle, and then from the radius, the circumference of the circle can be calculated. A = πr2, \( r= \sqrt{\frac{A}{\pi}}\), and C = 2πr = 2\(\pi\sqrt{\frac{A}{\pi}}\).

What are the Units of the Circumference of a Circle?

The circumference of the circle is a one-dimensional linear quantity and it has the same units of that of the length. The units of the circumference of a circle could be m, inch, cm, feet. The circumference of a circle is related to other linear quantities such as the radius, and diameter of the circle.

What is the Perimeter of the Circle?

The perimeter of a circle is the same as the circumference of a circle. It is the total length of the outer boundary of the circle. The perimeter or circumference of a circle is the product of the constant pi and the diameter of the circle. It is a linear one-dimensional quantity and has units such as m, inch, cms, feet.

What Is the Value of Pi?

Pi is a constant value used for the measurement of the area and circumference of a circle or other circular figures. The symbol of pi is π and its numeric value is equal to 22/7 or 3.14.  Further, these numeric values are used based on the context of the equation.

What is the Difference Between the Diameter And the Circumference of a Circle?

The diameter of the circle is the largest chord and is passing through the center of the circle. The circumference of the circle is the length of the outer boundary of the circle. Both the diameter and the circumference are lengths and have linear units for measurement. Also, the circumference of the circle is equal to the product of the diameter and the constant pi.


       Solved Examples on Circumference of a Circle

Example 1: A garland woven with flowers needs to be stuck around a circular ring to decorate it. How long should the garland be so as to cover a ring of a radius of 28 cm?

Solution:

Given, Radius of the ring = 28 cm. To find the length of the garland, we have to find the circumference of the ring. The circumference of a circle is calculated using the formula: 2π r  = 2 × 22/7 × 28 = 176 cm. Therefore, the length of the garland is 176 cms.

Example 2: The circumference of a wheel is 440 cm. Find its radius and diameter.

Solution:

Given, Circumference of the wheel = 440 cm. Circumference of a circle = 2πr. Let the radius of the circle be R. 440 &=2πR,  440 = 2 × 22/7 × R;  R = 70 cm, Diameter = 2r, Diameter = 2 ×  70. Therefore, the radius is 70cm, and diamter is 140cm.

Example 3: The perimeter of a rectangular wire is 264 m. The same wire is bent into the shape of a circle. Find the radius of the circle formed.

Solution:

We know that the perimeter of the rectangle = Total length of the wire used = Circumference of the circle formed. Hence, Circumference of the circle formed = 264 m. Circumference of a circle  =2πr = 264m, r=42m. Therefore the Radius is 42m.

Example 4: Tom runs three rounds at a circular stadium field every day before starting his cricket practice. The diameter of the field is 28 m. How much does he run around the field every day?

Solution:

Since Tom runs around the circular field, we need to find the circumference of the field. Given: Diameter = 28 m. Radius = 28/2 = 14m,  because Diameter = 2r. Circumference of a Circle =2πr = 2 × 22/7 × 14 = 88m. Hence, the circumference of the field is 88 m. We know that Tom runs around the field thrice. Hence, we multiply the circumference by 3. 3 × 88 =264m. Therefore, Tom runs 264 meters.

Challenging Question

  • The diameter of the given semi-circular slice of pizza is 28 cm. What is the perimeter of this slice of pizza?

Practice Questions on Circumference of a Circle

Try the Questions for Circumference of a Circle in the worksheet given below. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 
  
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