Introduction
Good day students. Today we will be looking at the Perimeter of circles, semi-circles, and quarter-circles.
we start this lesson off by looking at the key terms of this lesson:
•Perimeter
•Radius
•Diameter
•Circumference
•Pi
•Perimeter
It is the continuous line forming the boundary of the shape. For example the perimeter of a rectangle.
•Radius
The Radius (r) of a circle is the distance from the center of the circle to the edge of the circle.
Radius is = half the diameter
•Diameter
The Diameter (d) of a circle is the distance from the edge of the circle, through the center of the circle, to the opposite edge of the circle.
The diameter is twice as long as the Radius.
•Circumference
The perimeter of a circle is called the Circumference (c) of the circle.
•Pi
The symbol for Pi is written as ‘π’ and is equal to 3.142
Task
Calculating the circumference of a circle.
•To calculate the circumference of a circle, we use one of the following formulas:
•Circumference = 𝜋 x diameter of a circle
Written as
C= 𝜋 x d
•Circumference = 2 x 𝜋 x Radius
Written as
C= 2 x 𝜋 x r
Use the above formulae to work through the given examples.
Example 1
Find the circumference of the circle with a radius of 8 cm.
Solution
Circumference = 2 x π x R = 2πR
= 2 x 3.14 x 8
= 50.24 cm.
Example 2
Calculate the circumference of a circle whose diameter is 70 mm
Solution
Circumference = π x D = π D
= 3.14 x 70
= 219.8 mm
Example 3
Calculate the perimeter of a circular flower garden whose radius is 10 m.
Solution
Circumference = 2 x π x R = 2πR
= 2 x 3.14 x 10
= 62.8 m.
Process
Ensure that you read the questions thoroughly before answering the questions.
Complete the following exercise by using the correct formula:
Questions
1.The diameter of the wheels of a bicycle is 100 cm. How many rotations will each wheel make to travel a distance of 157 meters?
2.A wire is shaped like a rectangle and has a length of 100 cm and a width of 50 cm is cut from it and folded to make a circle. Calculate the circumference and radius of the circle that is formed.
3.The radius of the wheels of a motorbike is 0.85 m. how far will the motorbike travel if the wheels of the motorbike make 1000 revolutions? Assume that the motorbike is moving in a straight line.
Evaluation
Students, please ensure that you have completed the exercise and worked through the given examples before using the memorandum to correct/check your answers.
Solution 1
Circumference = π D
= 3.14 x100
= 314 cm
To get the number of rotations of the wheel, one must divide the distance covered by the circumference of the wheel.
remember whenever using measurement we ensure that the measurements of the equation are all the same. So we convert 157 meters to cm before dividing, then we multiply 157 by 100 to get 15700 cm.
∴
Number of rotations= 15700 cm/314 cm
= 50 revolutions.
Solution 2
The circumference of the circle formed = the perimeter of the rectangular wire.
Perimeter of a rectangle = 2(L + W)
= 2(100 + 50) cm
= 2 x 150 cm
= 300 cm.
∴
The circumference of the circle is equal to 300 cm.
Now we calculate the radius.
Circumference = 2 π R
300 cm = 2 x π x R
300 cm = 2 x 3.14 x R
300 cm = 6.28R
Now we will divide both sides by 6.28.
R = 47.77 cm
So, the radius of the circle will be 47.77 cm.
Solution 3
we first find the circumference of the wheel.
Circumference = 2 π R
= 2 x 3.14 x 0.85
= 5.338 m.
in order for us to find the distance traveled, we multiply the circumference of the wheel by the number of revolutions that were taken.
Distance = 5.338 x 1000
= 5338 m
we then divide the meters by 1000 in order to get it to kilometers
= 5338/1000
=5.338
∴
the distance traveled is equal to 5.338 kilometers.
Conclusion
Thank you all for attending the lesson it is for both the benefits of the teacher and students that we attend and work through the exercises.
next week will be continuing the lesson linked to the current topic. the topic for next week is the Area of circles. semi-circles and quarter-circles.
Calculate (to 1 decimal place) the circumference of a circle of which:
1.The Radius is 10cm
2.The diameter is 25cm.
3.The Radius is 35cm.
4.The diameter 120.5cm
Credits
Teacher Page
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