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Circles: Area and Circumference

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Definitions Circumference: Distance around the outside of a circle Area: How many squares it takes to cover a circle

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Definitions Radius: A line segment that goes from the center of the circle to the edge of the circle. radius diameter Diameter: Goes from edge to edge through the middle. Diameter = 2 times radius or d = 2r Radius = ½ times diameter or r = d/2

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Definitions Pi: Measure of the distance around the circle / (divided by) the diameter or distance across the circle and you ALWAYS get 3.14159265358979323846... We round this to 3.14 and call it Pi or use the symbol for pi which is π.

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Definitions Circumference: If you know the diameter of a circle you can find the circumference by using this formula: C = pi · d or C = πd But what if you only know the radius? C = pi · 2 · r or C = 2πr

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Definitions Area: The number of squares it takes to cover a circle A = pi · r · r or A = πr² But what if you only know the radius? Divide the diameter in half to get the radius and then use the formula.

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Examples Example 1: The radius of a circle is 2 inches. What is the diameter? d = 2 · r d = 2 · (2 in) d = 4 in

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Examples Example 2: The diameter of a circle is 3 centimeters. What is the circumference? C = π· d C = 3.14 · 3 cm C = 9.42 cm

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Examples Example 3: The radius of a circle is 2 inches. What is the circumference? d = 2 · r d = 2 · (2 in) d = 4 in C = π · d C = 3.14 · (4 in) C = 12.56 in

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Summary The number π is the ratio of the circumference of a circle to the diameter. (π = C/r) The value of π is approximately 3.14. The diameter of a circle is twice the radius. Given the diameter or radius of a circle, we can find the circumference. The formula for diameter is d = 2 · r The formula for circumference is C = π · d

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