area of a circle simplification
DESCRIPTION
Comparison of the area of a circle with the area of the square containing it.TRANSCRIPT
The area of a circle
– a simplified approach
Compare the area of the circle to the area of the box it sits inside.
Compare the area of the circle to the area of the box it sits inside.
It’s clearly smaller, but by how much?
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.
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.
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.
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.
Procedure:
1.
2.
3.
Procedure:
1. Find the area of the box (this is D2)
2.
3.
Procedure:
1. Find the area of the box (this is D2)
2. Calculate ¾ of that number
3.
Procedure:
1. Find the area of the box (this is D2)
2. Calculate ¾ of that number
3. Increase that number by five percent
60 cm
60 c
m
Say the diameter is 60 cm
Example:
60 cm
60 c
m
Say the diameter is 60 cm
The area of the box is 3600 cm2
Example:
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:
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:
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:
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:
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:
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:
To be perfectly accurate,
A = p R2
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
A = ( p/4 ) D2
To be perfectly accurate,
A = p R2
A = p ( D/2 ) 2
A = ( p/4 ) D2
A = 3.14159/4 D2
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
END