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.

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.

Procedure:

Procedure:Find the area of the box (this is D2)

Procedure:Find the area of the box (this is D2)Calculate ¾ of that number

Procedure:Find the area of the box (this is D2)Calculate ¾ of that number Increase that number by five percent

Example:60 cmSay the diameter is 60 cm60 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm260 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm260 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm2Ten percent of that answer is 270 cm260 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm2Ten percent of that answer is 270 cm2Five percent is therefore 135 cm260 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm2Ten percent of that answer is 270 cm2Five percent is therefore 135 cm2Add 135 to 270060 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm2Ten percent of that answer is 270 cm2Five percent is therefore 135 cm2Add 135 to 2700The area of the circle is 2835 cm260 cm

Example:60 cmSay the diameter is 60 cmThe area of the box is 3600 cm2¾ of that is 2700 cm2Ten percent of that answer is 270 cm2Five percent is therefore 135 cm2Add 135 to 2700The area of the circle is 2835 cm260 cmThe answer is correct to about a quarter of one percent.

To be perfectly accurate,A = p R2

To be perfectly accurate,A = p R2A = p ( D/2 ) 2

To be perfectly accurate,A = p R2A = p ( D/2 ) 2A = ( p/4 ) D2

To be perfectly accurate,A = p R2A = p ( D/2 ) 2A = ( p/4 ) D2A = 3.14159/4 D2

To be perfectly accurate,A = p R2A = p ( D/2 ) 2A = ( p/4 ) D2A = 3.14159/4 D2Therefore A = (slightly more than) ¾ D2

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