**Circumference of a Circle**

The curved
boundary or rim of a circle which is equidistant from its centre is called
**circumference of a circle**. The circumference of a circle is also known as the
**perimeter of circle**.

In the given figure curve line ABCD is the circumference of the circle. It is generally denoted by letter C.

Let us do an experiment. Take a coin. Put it on the scale and roll it as shown in the figure below.

When rolling completes one round it travels the length equal to the
circumference of the coin. Repeat this activity for other circular objects.

In such
activity, if diameter of the object is 3.5 cm then circumference is 11 cm. If
diameter is 7 cm then circumference is 22cm. Similarly, if diameter is 14 cm
them circumference is 44cm. From the above measurements, we have found that.

11/3.5 = 22/7 = 44/14 = 3.14

The length of the
diameter of different circles are proportional to their respective
circumference. This constant ratio of circumference by diameter (C/d) = 3.14 is
denoted by Greek symbol π (pai). For our convenience we use, π = 22/7 = 3.14

or, C/d = π

or, C = πd

or, C = π × 2r [∵ d = 2r]

or, C
= 2πr

**∴** **C = ****πd** or **C = ****2****πr** is the formula to calculate the circumference of a circle
in terms of radius or diameter.

*Workout
Examples*

*Workout Examples*

*Example 1: **Find the circumference of the circle
having *

*a)
**diameter
= 14 cm *

*b) **radius = 3.5 cm*

*Solution:** a) Here,*

* Diameter (d) = 14 cm*

* Circumference (c) = ?*

* We know,*

* C = πd = 22/7 × 14
cm = 44 cm*

* b) Here,*

* Radius (r) = 3.5 cm*

* Circumference (c) = ?*

* We know,*

* C = 2πr = 2 × 22/7 ×
3.5 cm = 22 cm*

*Example 2: **Find the radius of the circle whose
circumference is 88 cm.*

*Solution:** Here,*

* Circumference (c) = 88 cm*

* Radius (r) = ?*

* We know,*

* C = 2πr*

* i.e. 88 = 2 × 22/7 × r*

* or, 88 = 44/7 × r*

* or, 88 × 7/44 = r*

* or, r = 14 cm*

*Example 3: **The radius of circular cricket ground is
35 m. Find the length of rope which is required to fence around it 3 times?*

*Solution:** Here,*

* Radius (r) = 35 m*

* Circumference (c) = ?*

* We know,*

* C = 2πr*

* = 2 × 22/7 × 35 m*

* = 220 m*

* **∴** 1 round = 220 m*

* **∴** 3 round = 3 × 220 m = 660 m*

* **∴** 660 m long rope is required to fence around the cricket
ground 3 times.*

*You can comment your
questions or problems regarding the circumference
or perimeter of a circle here.*

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