Perimeter of a Circle

The circumference of a circle is the perimeter of the circle. The circumference of a circle is the distance around the circle.

The circumference of a circle  =  πD

Where D is the diameter of the circle.

If r is the radius of the circle and D  =  2r then  

C = π × 2r
C  =  2πr   

Circumference which is also the perimeter of a circle

 =    \( \scriptsize \pi d \: or \: 2 \pi r \)

Note: the value of x   = \( \scriptsize 3.142 \\ \scriptsize or \: \normalsize \frac{22}{7} \\ \scriptsize \: or \: 3\frac{1}{7} \)

Example 7.7.1:

Calculate the perimeter of a circle of radius 7 cm. Use the value of  \( \frac{22}{7}\scriptsize \: for \: \pi \)

Solution:

Perimeter   =   Circumference    =    \( \scriptsize 2 \pi r \)

= \( \scriptsize 2 \: \times \: \normalsize \frac{22}{7}\scriptsize \: \times \: 7 \)

= \( \scriptsize 2 \: \times \: \normalsize \frac{22}{\not{7}}\scriptsize \: \times \: \not{7} \)

= \( \scriptsize 2 \: \times \: 22 \)

= \( \scriptsize 44\:cm \)

Example 7.7.2: 

Calculate the perimeter of a circle if its:

(a) Diameter is 42 m
(b) Radius is  35 cm  

\( \scriptsize \left( \scriptsize \pi = \normalsize \frac{22}{7} \right) \)

(b) Radius is  35 cm  

Perimeter = 2πr 

= \( \scriptsize 2 \: \times \: \normalsize \frac{22}{7} \scriptsize\: \times \: 35 \)

= \( \scriptsize 2 \: \times \: 22 \: \times \: 5 \)

= \( \scriptsize 44 \: \times \: 5 \)

= \( \scriptsize 120 \:cm \)