How to Calculate the Area of a Circle
Identify the radius of a circle., Square the radius., Multiply by pi., Report your result.
Step-by-Step Guide
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Step 1: Identify the radius of a circle.
The radius is the length from the center of a circle to the edge of the circle.
You can measure this in any direction and the radius will be the same.
The radius is also one half of the diameter of a circle.
The diameter is the line segment that passes through the center and connects opposite sides of the circle.The radius will generally be provided to you.
It can be difficult to measure to the exact center of a circle, unless the center is already marked for you on a circle drawn on paper.
For this example, assume that you are told that the radius of a given circle is 6 cm. -
Step 2: Square the radius.
The formula to find the area of a circle is A=πr2{\displaystyle A=\pi r^{2}}, where the r{\displaystyle r} variable represents the radius.
This variable is squared.Do not get confused and square the entire equation.
For the sample circle with radius, r=6{\displaystyle r=6}, then r2=36{\displaystyle r^{2}=36}. , Pi, written symbolically with the Greek letter π{\displaystyle \pi }, is a mathematical constant that represents the ratio between the circumference and the diameter of the circle.As a decimal approximation, π{\displaystyle \pi } is approximately
3.14.
The true decimal value continues on infinitely.
For an exact statement of the area of a circle, you will usually report your answer using the symbol π{\displaystyle \pi } itself.For the given example with a radius of 6 cm, the area is calculated as:
A=πr2{\displaystyle A=\pi r^{2}} A=π62{\displaystyle A=\pi 6^{2}} A=36π{\displaystyle A=36\pi } or A=36(3.14)=113.04{\displaystyle A=36(3.14)=113.04} , Remember that a calculation of area is going to be reported in “square” units.
If the radius was measured in centimeters, the area will be in square centimeters.
If the radius was measured in feet, the area will be in square feet.
You should also know whether to report your result using the symbol π{\displaystyle \pi } or the numerical approximation.
If you do not know, then report both.For the sample circle with a radius of 6 cm, the area will be either 36π{\displaystyle \pi } cm2 or
113.04 cm2. -
Step 3: Multiply by pi.
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Step 4: Report your result.
Detailed Guide
The radius is the length from the center of a circle to the edge of the circle.
You can measure this in any direction and the radius will be the same.
The radius is also one half of the diameter of a circle.
The diameter is the line segment that passes through the center and connects opposite sides of the circle.The radius will generally be provided to you.
It can be difficult to measure to the exact center of a circle, unless the center is already marked for you on a circle drawn on paper.
For this example, assume that you are told that the radius of a given circle is 6 cm.
The formula to find the area of a circle is A=πr2{\displaystyle A=\pi r^{2}}, where the r{\displaystyle r} variable represents the radius.
This variable is squared.Do not get confused and square the entire equation.
For the sample circle with radius, r=6{\displaystyle r=6}, then r2=36{\displaystyle r^{2}=36}. , Pi, written symbolically with the Greek letter π{\displaystyle \pi }, is a mathematical constant that represents the ratio between the circumference and the diameter of the circle.As a decimal approximation, π{\displaystyle \pi } is approximately
3.14.
The true decimal value continues on infinitely.
For an exact statement of the area of a circle, you will usually report your answer using the symbol π{\displaystyle \pi } itself.For the given example with a radius of 6 cm, the area is calculated as:
A=πr2{\displaystyle A=\pi r^{2}} A=π62{\displaystyle A=\pi 6^{2}} A=36π{\displaystyle A=36\pi } or A=36(3.14)=113.04{\displaystyle A=36(3.14)=113.04} , Remember that a calculation of area is going to be reported in “square” units.
If the radius was measured in centimeters, the area will be in square centimeters.
If the radius was measured in feet, the area will be in square feet.
You should also know whether to report your result using the symbol π{\displaystyle \pi } or the numerical approximation.
If you do not know, then report both.For the sample circle with a radius of 6 cm, the area will be either 36π{\displaystyle \pi } cm2 or
113.04 cm2.
About the Author
Carol Allen
Carol Allen specializes in lifestyle and practical guides and has been creating helpful content for over 2 years. Carol is committed to helping readers learn new skills and improve their lives.
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