1. What is the Circumference?
The circumference of a circle is the total distance around the circle. It is similar to the perimeter of a polygon, but since a circle is curved, we use a special formula involving \(\pi\).
In simple words, if you walk around a circular park once, the distance you walk is the circumference.
2. Formula for Circumference
The circumference depends on the radius or diameter of the circle.
2.1. Using Radius
C = 2\pi r
Here, \(r\) is the radius of the circle.
2.2. Using Diameter
C = \pi d
Since \(d = 2r\), both formulas give the same result.
3. Where Does \(\pi\) Come From?
The number \(\pi\) is a constant that represents the ratio of the circumference of a circle to its diameter.
\dfrac{C}{d} = \pi
No matter the size of the circle, this ratio is always the same.
4. Example Calculations
Here are simple examples to see how the formula works:
4.1. Example 1
Find the circumference of a circle with radius \(7\text{ cm}\).
C = 2\pi r = 2 \times \pi \times 7 = 14\pi\text{ cm}
4.2. Example 2
Find the circumference when the diameter is \(20\text{ cm}\).
C = \pi d = 20\pi\text{ cm}
5. Approximation of the Circumference
Since \(\pi\) is an irrational number, we use approximations for real-life measurements:
- \(\pi \approx 3.14\)
- \(\pi \approx \dfrac{22}{7}\) (common in NCERT)
These give practical values for circumference calculations.
6. Relationship with Real Life
Knowing how to calculate circumference is useful in situations like:
- Measuring circular tracks or playgrounds
- Finding how far a wheel travels in one rotation
- Computing boundary lengths of circular objects
- Determining lengths of circular fences or borders