Circumference of Circle

The circumference of a circle is the distance around the boundary of a circle. It is also called the perimeter of a circle, and just as the perimeter of a square tells you how long the border is, the circumference of a circle tells you about the length of the circle boundary.

In this article, we will learn about the circumference of a circle, its formula, and the steps to find the circumference. From solving math problems to applying these formulas practically, this article will make the topic simple and fun.

 

Table of Contents

• What is Circumference?
• Formula for Circumference of Circle
• Area and Circumference of Circle
• Examples on Circumference of Circle
• Fun Fact About π (Pi)
• Real-Life Examples of Circumference
• Conclusion
• FAQs on Circumference of Circle

 

What is Circumference?

The circumference is the total distance around a circle. It’s like walking along the outer edge of a round field. In math, the circumference is the same as the perimeter of a circle.

So, when we say “circumference of a circle,” we mean the complete curved boundary of the circle. It is measured in units of length like centimeter, meter, feet, etc.

 

Circumference of Circle Formula

Before learning about circumference it is important to know in details about radius, diameter and center of a circle as knowing these properties of circles will help you grasp the concepts better.

Centre of a Circle: The centre point or the point in the middle of circle that is equidistant from any point on its boundary is called the centre of a circle.

Radius of a Circle: The radius of a circle is a distance from the centre to any point on the circle.

Diameter of a Circle: A straight line passing through the centre, touching two points on the circle. It’s twice the radius.

Circumference of Circle: The boundary or the outer line of the circle. The standard formula to find the circumference of a circle is:

Circumference (C) = 2πr

Where:

• π (pi) is a special math constant that represents the ratio of circle's circumference to its diameter. The value of π (pi) is approximately equal to 3.14159

• r is the radius of the circle (the distance from the center to the edge)

So, if you know the radius, you can find the circumference easily by multiplying it with 2 and π.

Another formula to find the circumference of a circle is πd, where d is the diameter of the cirlce and is twice the length of the radius. 

So, there are actually two main formulas you can use to find the circumference of a circle:

1. If you know the radius (r):
   C = 2πr

2. If you know the diameter (d) (which is twice the radius):
   C = πd

Both formulas give the same result. You can use whichever one is easier based on the information you have.

 

Area and Circumference of Circle

Besides the circumference, you might also need to find the area of a circle that is, how much space it covers inside the boundary.

Here are both formulas:

• Circumference:
  C = 2πr

• Area:
  A = πr²
  
  

So, the area of circumference formula doesn’t really exist because area and circumference are two different things:

• Circumference = boundary length

• Area = space inside the circle

 

Examples on Circumference of Circle 

Example 1: What will be the circumference of a circle with 5 cm radius?

Solution: We have a circle with radius = 5 cm.

• Circumference = 2 × π × 5 = 2 × 3.14 × 5 = 31.4 cm

• Area = π × 5² = 3.14 × 25 = 78.5 cm²

So you’ve now calculated both how far it is around the circle, and how much space it covers inside!

 

Example 2: Find the circumference of a circle with 3 cm radius.

Solution: 

Radius of circle = 3 cm.

Formula to calculate the Circumference of circle is:

Circumference = 2 × π × 3 = 2 × 3.14 × 3 = 18.84 cm

 

Fun Fact About π (Pi)

Did you know that π (pi) is a never-ending number? It goes on forever without repeating. Most people use 3.14 for easy calculations, but the actual value starts like this:

π = 3.1415926535... and so on!

It’s one of the most famous numbers in math!

 

Real-Life Examples of Circumference

1. Bicycle Wheel:
   If the wheel has a radius of 14 inches, the distance around the wheel is its circumference.
   C = 2 × 3.14 × 14 = 87.92 inches

2. Round Table:
   If a circular table has a diameter of 1 meter, the circumference is:
   C = π × 1 = 3.14 meters
   
   

This helps in measuring borders, ribbons around circles, tires, plates, and many round things!

 

Conclusion

Circumference of the circle is one of the key math skills. It helps us to gauge circular objects and answer geometry questions simply. Remember:

Circumference = distance around the circle

Area = space inside the circle

Assume π = 3.14 for rough estimates

 

Frequently Asked Questions on Circumference of Circle

Q1. What is 2πr in math?

Answer: It is the formula for the circumference of a circle.

2πr means 2 × π × radius. It tells how far it is around a circle.

 

Q2. What is the formula for circumference?

Answer: There are two formulas:

• C = 2πr (using radius)

• C = πd (using diameter)

Use whichever is easier based on what you know.

 

Q3. What is 3.14 in circumference?

Answer: 3.14 is the value used for π (pi) in simple calculations.

It helps us estimate the circumference using the formula.

 

Q4. What is the circumference and area of a circle?

Answer: If radius = r:

• Circumference = 2πr

• Area = πr²

Both are basic circle formulas in math.

 

Q5. What is the rule for area and circumference?

Answer: 

• Use C = 2πr for circumference

• Use A = πr² for area
  Both depend on the radius and the number π.

 

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