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## JSS1: MATHEMATICS - 2ND TERM

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Lesson 7, Topic 7
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# Perimeter of a Circle

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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 = π2r
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 1:

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

Solution:

Perimeter   =   Circumference    =    $$\scriptsize 2 \pi r$$

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

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

= $$\scriptsize 2 \: \times \: 22$$

= $$\scriptsize 44cm$$

### Example 2:

Calculate the perimeter of a circle if its:

(a) Diameter is 42m

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

Solution:

(a) Diameter is 42m

Perimeter   =    πD

= $$\frac{22}{7} \scriptsize \: \times \: 42$$

= $$\scriptsize 22 \: \times \: 6$$

= $$\scriptsize 132cm$$

= $$\scriptsize 2 \: \times \: \normalsize \frac{22}{7} \scriptsize\: \times \: 35$$
= $$\scriptsize 2 \: \times \: 22 \: \times \: 5$$
= $$\scriptsize 44 \: \times \: 5$$
= $$\scriptsize 120 \:cm$$