Introduction
HELLO STUDENTS!!!
Today we will be talking about the CIRCLE
A circle is a round shape figure that has no vertices and measures 360º.
Take a look at the circle below.
A circle generally has eight (8) parts namely; Radius, Sector, Segment, Arc, Tangent, Chord, Circumference and Diameter.
Circumference of a Circle
The circumference of a circle is the distance along its outer rim or perimeter. The circumference is calculated using the formula πd or 2πr. (i.e r is the radius and d is the diameter)
Area of a Circle
The area of a circle refers to its surface area and is calculated using the formula π*r*r. (i.e r is the radius)
Task
Jeana recently built her dream house in Spring Farm, Bontego May. The dining and living rooms are circular in shape, having the same dimensions. The dining room has a line running through the centre touching two points on the walls that measure 100cm. Jeana needs to calculate the surface area and perimeter of the two rooms in order to calculate the number of tiles and the length of strips needed to tile and decorate the rooms respectfully. Let’s help Jeana’s mother with this calculation.
Process
Step 1
Given that this is a worded problem you want to identify what it is asking of you. In this case, you are being asked to calculate the area along with the circumference of the two rooms.
Step 2
Secondly, you want to make a graphic representation of the information given to you, so that's two (2) circles both having a diameter of 100cm
Step 3
Identify the formulae that will be used in making the calculation.
Area
(π*r*r)
Circumference
(2*π*r)
Step 4
Application of the formulae. Given that the living and dining rooms have the same dimensions we can calculate the area and circumference for each then multiply them by two (2). (N.B: The diameter is twice the length of the radius)
Area
2(π*r*r)
2(22/7*50*50)
2(55,000/7)
= 15,714.29 squared cm
Circumference
2(2πr)
2(2*22/7*50)
2(2200/7)
=629 cm (rounded to the nearest whole number)
Evaluation
This question values 5 marks. Marks will be allotted for each step as follows;
Step 1
1.5 marks will be awarded for understanding that the question is requiring you to calculate the area and circumference of both rooms.
Step 2
No mark will be awarded for this step as it is optional for students to make graphical representations.
Step 3
1 mark will be awarded for stating the formula accurately for calculating the area and circumference.
Step 4
2.5 marks will be awarded for precise calculations and the correct answer to the question.
Conclusion
In calculating the area and circumference Jeana will know the exact amount of material needed to decorate her home. This is the power of Mathematics being applied in reality. Have an open mind when you attend your next Mathematics class as MATHEMATICS IS FUN.
Credits
Ashutosh. (2020, October 30). What is a circle and its properties? (definition, formulas, examples). GMAT. Retrieved December 01, 2021, from https://e-gmat.com/blogs/circle-properties-circle-formulas-circle-area-…
Teacher Page
This Webquest is a valuable tool to use with students. It allows them to work at their own pace either individually or collaboratively. This Webquest is a fun, research-based tool to help students learn more detailed information about THE CIRCLE and create a greater sense of importance. Webquests also provide variety in the classroom routine, help students improve their internet and researching skills, and provide excellent opportunities to explore and learn. Youths are always interacting with technology in some way, whether it be messaging, social networking, blogging, listening to music, doing assignments or even shopping. Technology is an essential part of their lives therefore, it is more beneficial to teach students using technology instead of the clichéd methods used over the years.