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8.7 Circumference and Area of Circles
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Definition A circle is the set of all points in a plane that are the same distance from a given point, called the center of the circle. A circle with center is called “circle,” or.
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Terms The distance from the center to a point on the circle is the radius. The distance across the circle, through the center, is the diameter. The circumference of a circle is the distance around the circle.
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Terms radius diameter circumference r d c
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Terms For any circle, the ratio of the circumference to its diameter is denoted by the Greek letter π, or pi. The number π is 3.14159…, which is an irrational number, which neither terminates nor repeats. An approximation of 3.14 is used for π.
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Circumference of a Circle Words Circumference = π (diameter) = 2π (radius) Symbols C = πd or C = 2πr
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Finding Circumference Find the circumference of the circle. 4 in. C = πd or C = 2πr C = 2πr = 2π(4) = 8π = 8(3.14) = 25.12 in.
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Area of a Circle Words Area = π (radius) 2 Symbols A = πr 2
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Finding Area of a Circle Find the Area of the Circle A = πr 2 A = π(7) 2 A = π(49) A = (3.14)(49) A = 153.94 cm 2 7 cm
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Using the Area of a Circle Find the radius of a circle with an area of 380 square feet. A = πr 2 380 = πr 2 380/ π = r² 120.96 ≈ r² 11 ft ≈ r r
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Central Angles An angle whose vertex is the center of a circle is a central angle of the circle. A region of a circle determined by two radii and a part of the circle is called a sector of the circle. r ө
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Central Angles Because a sector is a portion of a circle, the following proportion can be used to find the area of a sector. r Area sector Area circle Measure central angle Measure circle = ө
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