Circumference

Mitchell and his friends have taken the responsibility of planting new trees in the circular compound of the school.

For doing that, they need to understand the concept of the circumference.

Let’s learn about circumference, circumference definition, circumference geometry definition, circumference of a circle formula, circumference equation circumference of circle. 

Check-out the interactive simulation to know more about the lesson and try your hand at solving a few interactive questions at the end of the page.

Lesson Plan

What is Circumference?

The Circumference is a closed curve where all points are at the same distance from the center.

The circumference of a circle is also known as the perimeter of a circle.

Now let’s learn about the elements that make up circumference.

Center

The Center is a point which is at a fixed distance from any other point from the circumference.

Diameter

Diameter is the distance across the circle through the center.

Radius

The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.

These are the three most important elements of a circle.

Circumference

Examples:

Wheel of car, full moon, ring


What is Circumference of a Circle

The Circumference of a circle is its boundary or the length of the complete one of a circle.

Let us understand this concept using an example.

Consider a circular park as shown below

Circumference

Philip starts running from point "A" and reaches the same point after taking

one complete round of the park. There is a distance that is covered by him.

This distance or boundary is called the Circumference of the park which is in the shape of a circle.

Look at the following simulation and see how the length of the circumference changes with its radius.


Circumference Formula      

        To get the circumference formula we have to know about "Pi".

Pi is a special mathematical constant with a value approximated to \(3.145\) or \(\frac{{22}}{7}\)

It is the ratio of circumference to diameter when  \(C = \pi D\).

The Formula for the Circumference of a Circle 

The formula circumference of a circle can be calculated using the diameter D of the circle and the value of \(\pi \).

\[Circumference = \pi  \times D\]

While using this formula, if we do not know the value of the diameter, we can find it using the radius.

That is if the radius is known,

\(Diameter = 2 \times r\)

Another way to calculate the circumference of a circle is by using the formula

\(Circumference = 2\pi r\)

Drag and see the relation between the radius and circumference of a circle.

 
important notes to remember
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 \(\pi  = \frac{{22}}{7}\) or 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, \(Diameter = 2 \times Radius\).
  • 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.
  • \(Circumference = \pi \times D\);  \(Circumference = 2\pi r\)

Solved Examples

Example 1

 

 

To celebrate Christmas, some children have decided to create a garland. Flowers need to be stuck around a circular ring to decorate it. How long should the garland be so as to cover a ring of radius 14 inch?

Circumference

Solution

 Given:  Radius of the ring = 14 inch

            To find the length of the garland, we have to find the circumference of the ring.

\[\begin{align}
 Circumference &= 2\pi r \\[0.2cm]
  &= 2 \times \frac{{22}}{7} \times 14 \\[0.2cm] 
  &= 88 inch \\ 
 \end{align}\]

\(\therefore\) length of the garland is \(88\) inches
Example 2

 

 

The rotation of the wheel cart has a circumference of 220 inches. Find its radius.

Circumference

Solution

Circumference of wheel = \(220\) inch

\[\begin{align}
 2\pi r &= 220 \\[0.2cm] 
 2 \times \frac{{22}}{7} \times r &= 220 \\[0.2cm] 
 r &= \frac{{220 \times 7}}{{22 \times 2}} \\[0.2cm] 
 r &= 35 \\[0.2cm] 
 \end{align}\]

\(\therefore\) Radius of the wheel is \(35\) inches
Example 3

 

 

Sam runs four rounds at a circular stadium field every day before his cricket practice. The diameter of the field is 98 ft. How much does he run around the field every day?

Circumference

Solution

 Since Sam runs around a circular field, we need to find the circumference of the field.

Given :  Diameter = \(98ft\)

            Radius = \(\begin{align}\frac{{98}}{2} =49ft\end{align}\)

\(\begin{align} \text{Circumference of a circle} \!&= 2\pi r \\[0.2cm] &= 2 \times \frac{{22}}{7} \times 49 \\[0.2cm] &= 308ft \end{align}\)

\(\therefore\) Everyday Sam runs \(308\) ft
Example 4

 

 

Find the radius of Cake A whose circumference is 5 times that of the circumference of Cake B with a diameter of 12 inches.

Circumference

Solution

Diameter of Cake B = \(12 inch\)

Therefore, Radius of Cake B = \(6 inch\)

 \(\begin{align} \!\text{Circumference of Cake B}\!&=\! 2\pi r \\[0.2cm] &=\! 2 \times \frac{{22}}{7} \times 6 \\[0.2cm] &=\! \frac{{264}}{7} \\[0.2cm]  \end{align}\)

Since, the circumference of Cake A is 5 times that of circumference of Cake B, we get = \(\begin{align}5 \times \frac{{264}}{7} \end{align}\)

Circumference of Cake A = \(\begin{align}\frac{1320}{7}\end{align}\)

Now, let's find the radius of Cake A. 

Let the Radius of Cake A be R cm.

Circumference of Cake A:

\[\begin{align}
 \frac{{1320}}{7}& = 2\pi R \\[0.2cm] 
 \frac{{1320}}{7} &= 2 \times \frac{{22}}{7} \times R \\[0.2cm] 
 R &= 30 inch \\ 
 \end{align}\]

\(\therefore\) radius of Cake A is \(30\) inches
Example 5

 

 

Jenifer has a rectangular wire whose perimeter is 264 inches. She bends the same wire into the shape of a circle. Find the radius of the circle formed.

Circumference

Solution

We know that perimeter of the rectangle = Total length of the wire

Length of the wire used = Circumference of the circle formed 

Hence, Circumference of the circle formed = 264 inch

\[\begin{align}
 \text{Circumference of a circle }&= 2\pi r \\[0.2cm] 
 2\pi r &= 264 \\[0.2cm] 
 2 \times \frac{{22}}{7} \times r &= 264 \\[0.2cm] 
 r &= \frac{{264 \times 7}}{{2 \times 22}} \\[0.2cm] 
 r &= 42 \\[0.2cm] 
 \end{align}\]

\(\therefore\) radius of the circle is \(42\) inches
 
Challenge your math skills
Challenging Questions
  • Regina and her mom are jogging around a semi-circular park. If the diameter of this park is 70 yd, what is the circumference of this park?

 

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result

 
 
 
 
 
 

Let's Summarize

We hope you enjoyed learning about Circumference with the simulations and practice questions. Now you will be able to easily solve problems on circumference definition, circumference geometry definition, circumference of a circle formula, circumference equation, and circumference of circle.

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Frequently Asked Questions (FAQs)

1. How to find circumference?

\(Circumference = \pi  \times D\) 

and if radius is given, then  \(Circumference = 2\pi r\)

2. What is the circumference of a circle with diameter 4 cm?

\[\begin{align}
Circumference &= \pi D \\[0.2cm] 
&= \frac{{22}}{7} \times 4 \\[0.2cm] 
&= \frac{{88}}{7}cm \\ 
\end{align}\]

3. How to calculate the circumference of a circle?

Circumference of a circle can be calculated as,  \(C = 2\pi R\)

For Example : For Radius = 7inch 

\[\begin{align}
 Circumference &= 2\pi r \\[0.2cm] 
  &= 2 \times \frac{{22}}{7} \times 7 \\[0.2cm] 
  &= 44 inch \\[0.2cm] 
 \end{align}\]

4. How to calculate the diameter from circumference?

Diameter from circumference can be calculated as , \(\begin{align} Diameter = \frac{{Circumference}}{\pi }\end{align}\)

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