Download - Area Of A Circle Simplification
![Page 1: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/1.jpg)
The area of a circle
– a simplified approach
![Page 2: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/2.jpg)
Compare the area of the circle to the area of the box it sits inside.
![Page 3: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/3.jpg)
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
![Page 4: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/4.jpg)
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
The diamond on the inside of the circle covers half the area of the box.
![Page 5: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/5.jpg)
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
The diamond on the inside of the circle covers half the area of the box.
The circle looks like it covers about ¾ of the box.
![Page 6: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/6.jpg)
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
The diamond on the inside of the circle covers half the area of the box.
The circle looks like it covers about ¾ of the box.
That estimate is often good enough, depending on your purpose.
![Page 7: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/7.jpg)
However, to be much more precise, increase that estimate by five percent.
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
The diamond on the inside of the circle covers half the area of the box.
The circle looks like it covers about ¾ of the box.
That estimate is often good enough, depending on your purpose.
![Page 8: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/8.jpg)
Procedure:
1.
2.
3.
![Page 9: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/9.jpg)
Procedure:
1. Find the area of the box (this is D2)
2.
3.
![Page 10: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/10.jpg)
Procedure:
1. Find the area of the box (this is D2)
2. Calculate ¾ of that number
3.
![Page 11: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/11.jpg)
Procedure:
1. Find the area of the box (this is D2)
2. Calculate ¾ of that number
3. Increase that number by five percent
![Page 12: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/12.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
Example:
![Page 13: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/13.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
Example:
![Page 14: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/14.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Example:
![Page 15: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/15.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Ten percent of that answer is 270 cm2
Example:
![Page 16: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/16.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Ten percent of that answer is 270 cm2
Five percent is therefore 135 cm2
Example:
![Page 17: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/17.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Ten percent of that answer is 270 cm2
Five percent is therefore 135 cm2
Add 135 to 2700
Example:
![Page 18: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/18.jpg)
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Ten percent of that answer is 270 cm2
Five percent is therefore 135 cm2
Add 135 to 2700
The area of the circle is 2835 cm2
Example:
![Page 19: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/19.jpg)
Say the diameter is 60 cm
The area of the box is 3600 cm2
¾ of that is 2700 cm2
Ten percent of that answer is 270 cm2
Five percent is therefore 135 cm2
Add 135 to 2700
The area of the circle is 2835 cm2
60 cm
60 c
m
The answer is correct to about a quarter of one percent.
Example:
![Page 20: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/20.jpg)
To be perfectly accurate,
A = p R2
![Page 21: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/21.jpg)
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
![Page 22: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/22.jpg)
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
A = ( p/4 ) D2
![Page 23: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/23.jpg)
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
A = ( p/4 ) D2
A = 3.14159/4 D2
![Page 24: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/24.jpg)
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
A = ( p/4 ) D2
A = 3.14159/4 D2 Therefore A = (slightly more than) ¾ D2
![Page 25: Area Of A Circle Simplification](https://reader033.vdocument.in/reader033/viewer/2022061201/547960a7b37959492b8b4705/html5/thumbnails/25.jpg)
END