2.1 The characteristics of a circle

Mathematics

Grade 8

Rational numbers, circles and triangles

Module 13

The characteristics of a circle

Activity 1

Discovering the characteristics of a circle

[lo 3.1, 4.2.1, 3.4]

1. Try to copy the following design, using a pair of compasses only:

2. Draw a circle of any size. Refer to a textbook or any other source of information to help you indicate the following on the circle:

2.1 Centre: T

2.2 Diameter (Name it PQ .)

2.3 Radius: TS

2.4 Any arc: FG

2.5 Sector: PTW (shade this portion.)

2.6 Chord: KL

2.7 Use a coloured pencil to indicate where you would determine the circumference of the circle.

3. Refer to your sketch to answer the following questions:

3.1 What is characteristic of TW , PT , TS and TQ ?

3.2 Measure $P\hat{T}W$ .

3.3 What is the size of $P\hat{T}Q$ ?

3.4 What do we call this type of angle?

4. Construct the following with the help of a pair of compasses:

4.1 a circle with a diameter measuring 4 cm

4.2 a circle with a radius of 1,5 cm

5. How would you go about constructing a circle of 4 m?

• Plan:

Activity 2

Discovering the circumference of a circle and dealing with related problems

[lo 4.2.2, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5.1]

1. Make use of about four bottles / cups of different sizes. Use a length of string and measure the diameter of each of the bottles to complete the following table:

• What is noticeable in the last column?

circumference ÷ diameter

1.2 What is the term used for the answer in the last column?

1.3 Name two values that can be used for π: ...................... or ......................

1.4 Which formula can therefore be used to calculate the circumference of any circle?

2. We could also deduce this formula from a circle by proceeding as follows:

2.1 Draw a circle with centre P and radius 25 mm on a sheet of paper.

2.2 Cut out the circle and place a mark anywhere on the edge of the cut circle.

2.3 Draw a line (use a ruler) across the remaining area of the sheet of paper. Roll the circle (cut out disk) on its edge along this line (place the mark on the edge of the circle at the beginning of the ruled line. Mark the spot where the rotation is completed on the line when the rolled circle has completed a full rotation.

2.4 Use your ruler to measure the marked distance.

• Distance: ......................... mm

2.5 What term would we use to describe the distance that was measured in 2.4?

2.6 Use your calculator to calculate the following:

• circumference ÷ diameter = ..................... ÷ ..................... = ........................

2.7 What term do we use to describe the answer that you have obtained?

3. What do we actually mean when we say that the wheel of a bicycle has completed a full rotation?

4. Write the formula for calculating the circumference of a circle on the following line and answer the questions that follow:

• Circumference = ..................................................

4.1 How would you calculate the radius of a circle when the circumference is provided?

• Radius ( R ) = ..................................................