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## JSS1: MATHEMATICS - 2ND TERM

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#### Quizzes

Lesson 8, Topic 7
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# Area of a Circle

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Area of a circle  =  $$\scriptsize \pi r^2$$

We can also find the area given the diameter

the radius of a circle is half of its diameter

r = $$\frac{d}{2}$$

We can substitute this into Area of a circle   =  $$\scriptsize \pi r^2$$

Therefore Area = $$\scriptsize \pi \: \times \: \normalsize \frac{d}{2} \scriptsize \: \times \: \normalsize \frac{d}{2} \\ = \frac{\pi d^2}{4}$$

To calculate the Area of a Semi-circle, divide the area of a circle by 2 (as two semi-circles make a circle). We get, $$\frac{1}{2} \; \times \; \scriptsize \pi r^2$$

To calculate the Area of a Quadrant, divide the area of a circle by 4 (as four quadrants make a circle). We get, $$\frac{ \pi r^2}{4}$$

### Example 1:

Find the area of a circle with a radius of 3.5cm.

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

Solution:

r = $$\scriptsize 3.5 \: or \: \normalsize \frac{35}{10}$$

Area of a circle  =  $$\scriptsize \pi r^2$$

Area of a circle  =  $$\frac{22}{7} \; \times \; \frac{35}{10} \; \times \; \frac{35}{10}$$

=  $$\frac{22 \; \times \; 5 \; \times \; 35}{10 \; \times \; 10}$$

=  $$\frac{3850}{100}$$

=  $$\scriptsize 38.50 cm^2$$

or

⇒ $$\scriptsize \pi r^2 = \normalsize \frac{22}{7} \scriptsize\; \times \; 3.5 \; \times \; 3.5$$

= $$\frac{269.5}{7}$$

=  $$\scriptsize 38.5 cm^2$$

### Example 2:

Find the area of a semicircle with a diameter of 22mm.

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

Note: Radius = $$\frac{diameter}{2}$$

r = $$\frac{d}{2}$$

From the question, d  =  22 mm

r = $$\frac{d}{2}$$

r = $$\frac{22}{2}$$

r = 11 mm

Area of a semicircle   =   ½  x  area of a circle

Area of a semicircle   =   ½  x  πr2.

Area of a semicircle   =   $$\frac{1}{2} \; \times \; \frac{22}{7} \; \times \; \scriptsize (11)^2$$

=   $$\frac{1}{2} \; \times \; \frac{22}{7} \; \times \; \scriptsize 11 \; \times \; 11$$

= $$\frac{11\; \times \; 11 \; \times \; 11}{7}$$

= $$\frac{1331}{7}$$

Area of a semicircle = 190.1 mm2

or

Area = $$\frac{\pi d^2}{4}$$

d = 22 mm

Therefore, Area = $$\frac{\pi \; \times \; 22^2}{4}$$

= $$\frac{ \frac{22}{7} \; \times \; 22 \; \times \; 22}{4}$$

= $$\frac{ 22 \; \times \; 22 \; \times \; 22}{28}$$

Area = $$\frac{ 10648}{28}$$

Area = 380.3

Area of a semicircle   =   ½  x  area of a circle.

Area of a semicircle = $$\frac{1}{2} \; \times \; \scriptsize 380.3$$

Area of a semicircle = 190.1 mm2

### Example 3:

Find the area of a circular shape which has a circumference of 21.89m.

$$\left ( \scriptsize \pi = 3.14 \right)$$

Solution:

The circumference of a circle is given by:

C = πd

d = $$\frac{C}{\pi}$$

C  =   21.89m,

π = 3.14

d = $$\frac{21.89}{3.14}$$

d = 6.97m

So radius   =  $$\frac{d}{2}$$

=  $$\frac{6.97}{2}$$

= 3.49m

Area of a circle  = $$\scriptsize \pi r^2$$

= 3.14 × (3.49)2

= 3.14  ×  3.49  ×  3.49

= 38.2m

The area of the circle is 38.2m

### Example 4:

Calculate the area of each of the following shapes:

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

(a)

Area = πr2

Area of a semi-circle  = $$\frac{\pi r^2}{2}$$

radius is half of the diameter, from the question diameter, d = 28cm

∴ r = $$\frac{d}{2}$$

r = $$\frac{28}{2}$$

r = $$\scriptsize 14 \: cm$$

Area = πr2

Area = $$\frac{22}{7} \; \times \; \scriptsize 14 \; \times \; \times \; 14$$

= 22  ×  2  ×  14

= 616cm2

Area of semi-circle  = $$\frac{616cm^2}{2}$$

Area of semi-circle  = $$\scriptsize 308cm^2$$

(b)

Area of circle = $$\scriptsize \pi r^2$$

Area of quadrant  =  $$\frac{\pi r^2}{4}$$

⇒ $$\scriptsize \pi = \normalsize \frac{22}{7}\scriptsize, \; r = 7$$

Area = $$\frac{22}{7} \; \times \; \scriptsize 7 \; \times \; 7$$

= $$\scriptsize 22 \; \times \; 7$$

= $$\scriptsize 154cm^2$$

Area of a quadrant   = $$\frac{154}{4}$$

= $$\scriptsize 38.5cm^2$$

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