The material on this web-based lesson learned in sixth grade elementary school in semester I. This material is located on the third competency standards that calculate the area of a simple polygon, area of a circle, and the volume of a triangular prism. While the basic competence is calculate the area of a circle. At this time of learning we will discuss the value of π, the circumference and area of a circle.
Learning starts with contextual problem as follows:
Mom wants to decorate lid of can shaped circle to make it more beautiful. Mom decorates with lace on the edges and covering the top by using gift paper. What is the minimum length of lace and gift paper needed to decorate the lid of can?
In your opinion, what concept is related to problems above?
The above problem associated with the circumference of a circle for giving a lace and the area of a circle for giving gift paper. Therefore, in this learning we will learn how to find the value of π, the formula of circumference and area of a circle.
Before discussing about the value of π, circumference and area of a circle, we must remind what is circle and parts of circle first.
What is CIRCLE?
Circle is the set of all points in a plane that has an equal distance to a certain point, which is the central point.
Parts of Circle
Please run the following Applet
For the explanation of the parts of the circle please click here.
A. The Value of π and The Formula of Circle Circumference
Please do this activities in cooperation with your friends
- Collect circular things around you
- Measure the length of the diameter and circumference of the object. (You can measure it by using a rope or tape measure of tailor)
- Compare the length of the circumference by the diameter
Write down the results in the following table.
No |
Circumference |
Diameter |
C/D |
What is the value that you get from comparing the circumference by the diameter?
What is the formula of circle circumference that you conclude from the above activities?
For more details, please run the applet below
Based on previous activities have been carried out, it is known that
Circumference = 3 1/7× Diameter
Circumference = 3,14× Diameter
Value of 22/7 or 3,14 is a value or a constant called the value of π.
It can be concluded that the formula of circle circumference is:
B. The Formula of Circle Area
In finding the formula of circle area, we can use the formula of another plane figure. We can arrange the pieces or the sector of circle into various plane figure.
In your opinion, what are the plane figure can be formed?
Please do this activities in cooperation with your friends
- Look for objects around you in the form of a circle, for example the lid of can
- Sketch the object on the carton and divide into many sectors
- Arrange the sectors of circle into a plane figure that do you want.
- Find the formula of circle area from the formula of plane figure area by connecting the part of plane figure with the part of circle.
What is the formula of circle area that you get from the previous activity?
As an example, please run the applet below.
For further details, you may observe the following video
Based on the activities that have been carried out before, it can be concluded that:
Please try to arrange the sectors of circle into another plane figure and find the formula of circle area
After finding the formula of circumference and area of circle, answer the following question which is the context in the beginning of the learning.
Question:
Mom wants to decorate lid of can shaped circle to make it more beautiful. Mom decorates with lace on the edges and covering the top by using gift paper. What is the minimum length of lace and gift paper needed to decorate the lid of can if the radius is 14 cm.
After doing the previous activities, we can conclude:
For a better understanding material about the circumference and area of a circle, please do practice questions on the following website
http://www.ixl.com/math/geometry/area-and-circumference-of-circles
The learning activities have been implemented in one of primary school. To view the report, you can download it here.
The report of π value and the circumference of circle Indonesian version & English Version
The report of the area of circle Indonesian Version & English Version
Reference
______________ . Geogebratube. http://www.geogebratube.org/. Access on November 19^{th} 2012