Topic 8: The Circle

By the end of this topic, you will be able to:

(a) identify various parts of a circle.

(b) state and use the formula for circumference and area enclosed by a circle.

Keywords

• area
• centre
• circumference
• diameter
• formula
• radius

Introduction

In your daily life, you have often seen circle objects and shapes. If the Uganda currency coins of UGX 1000, UGX 500, UGX 200 and UGX 100 are traced on paper, a circular shape is obtained.

Also, most lids of containers like tanks, jerrycans and mineral water bottles when traced will give circular shapes. At primary school, you studied the properties of circles. In this topic, you will understand, justify and apply the formulae for the area and circumference of a circle.

8.1 Identifying parts of the circle.

Activity 8.1 Identifying Parts of the Circle

1. Draw four circles and identify the following parts on the different circles. (a) Centre

(b) Radius

(c) Diameter

(d) Circumference

2. (a) Draw a circle and on it, label the radius (r) and diameter (d).

(b) Take measurements and state the relationship between r and d.

3. Share your work with the rest of the class.

8.2 Stating and using the formula for circumference and area enclosed by a circle

8.2.1 Finding the circumference of a circle 1.

Activity 8.2 Generating the formula for the circumference of a circle

1. Collect at least 4 circular objects such as mineral water bottle tops, mugs etc. Measure the diameters and circumferences. You may use rulers and thread.
   • (a) Use the results obtained to fill in the table below.

(b) What do you notice from the results obtained?

2. Using your knowledge from primary school, what is the name of the ratio: circumference? diameter

3. How can you obtain circumference of a circle given the diameter?

8.2.2 Finding area of a circle

In the previous section, you have learnt that length of circumference, C of a circle is given by C = πd and that d = 2r. In this section, you will use this idea to justify the formula for area of a circle.

Activity 8.3 Generating the formula for area a circle

1. On a sheet of paper, draw a large circle. By drawing radii at equal intervals, cut the circle into equal pieces using suitable cutting materials.
2. Use glue to arrange the pieces into a rectangular shape with equal pieces on each scale.
3. Establish the area of the original circle from the area of the rectangular shape formed.

Exercise 8.1

1. Find the area of the circles whose radii are:
   • (a) 7 cm
   • (b) 14 cm
   • (c) 20 cm
   • (d) 30 cm
   • (e) 50 cm
   • (f) 60 cm
   • (g) 10 cm
   • (h) 28 cm
2. A circular disc of radius 3.5 cm is cut out of a rectangular sheet of paper. If the sheet of paper measures 15 cm by 8 cm, that remains