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Main Idea/Vocabulary circle center radius chord diameter Find the circumference and area of circles. circumference pi

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KC

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Example 1 Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. Answer:The circumference is about 15.7 feet. C = dCircumference of a circle C = 5 Replace d with 5. C = 5 This is the exact circumference. Use a calculator to find 5 × ENTER =

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1.A 2.B 3.C 4.D Example 1 A.38.5 in. B.31.4 in. C.22.0 in. D.19.7 in. Find the circumference of the circle. Round to the nearest tenth.

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Example 2 Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. Answer: The circumference is about 23.9 meters. C = 2 r Circumference of a circle C = 2 3.8Replace r with 3.8. C ≈ 23.9Use a calculator.

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1.A 2.B 3.C 4.D Example 2 A.9.4 m B.11.3 m C.18.5 m D.22.6 m Find the circumference of the circle. Round to the nearest tenth.

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KC

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Example 3 Find the Areas of Circles Find the area of the circle. Round to the nearest tenth. Answer: The area is about 28.3 square yards. A = r 2 Area of a circle A = 3 2 Replace r with 3. A = 9 Evaluate 3 2. A ≈ 28.3Use a calculator.

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1.A 2.B 3.C 4.D Example 3 A.12.6 ft 2 B.14.1 ft 2 C.15.3 ft 2 D.17.4 ft 2 Find the area of the circle. Round to the nearest tenth.

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Example 4 Find the area of the circle. Round to the nearest tenth. Answer: The area is about 78.5 square inches. Find the Areas of Circles A = r 2 Area of a circle A = 5 2 Replace r with half of 10 or 5. A = 25 Evaluate 5 2. A ≈ 78.5Use a calculator.

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1.A 2.B 3.C 4.D Example 4 A.42.7 cm 2 B.50.3 cm 2 C.52.1 cm 2 D.54.6 cm 2 Find the area of the circle. Round to the nearest tenth.

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Example 5 POOLS The Patels have a circular pool with a radius of 12 feet. They plan on installing a 4-foot-wide walkway around the pool. What will be the area of the walkway? To determine the area of the walkway, you must subtract the area of the pool from the area of the outer circle that includes the pool and the walkway.

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Example 5 Area of Outer Circle A = r 2 Area of a circle A = (16) 2 Replace r with or 16. A = 256 Evaluate 16 2.

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Example 5 Area of Pool A = r 2 Area of a circle A = 12 2 Replace r with 12. A = 144 Evaluate 12 2.

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Example 5 Area of Walkway Answer:The area of the walkway is about square feet. ≈ 256 – 144 ≈ Area of Outer Circle – Area of Pool

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1.A 2.B 3.C 4.D Example 5 A.62.8 ft 2 B.84.3 ft 2 C.99.2 ft 2 D ft 2 POOLS The Shoemakers have a circular pond with a radius of 4 feet. They plan on installing a 2- foot-wide walkway around the pond. What will be the area of the walkway?

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1.A 2.B 3.C 4.D Five Minute Check 1 A.145° B.125° C.55° D.35° Refer to the figure. Find m 1 if m 2 is 35°. (over Chapter 6)

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1.A 2.B 3.C 4.D Five Minute Check 2 A.L'(0, 2), M'(–2, 0), N'(2, 0) B.L'(0, 4), M'(–2,0), N'(2, 0) C.L'(4, 2), M'(2, 0), N'(6, 0) D.L'(4, –4), M'(2, –6), N'(6, –6) Find the coordinates of the vertices of triangle LMN with vertices L(2, –1), M(0, –3), and N(4, –3) translated by (–2, 3). (over Chapter 6)

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1.A 2.B 3.C 4.D Five Minute Check 3 A.J'(–4, 2), K'(–1, 2), L'(–1, 1), M'(6, 1) B.J'(–4, 2), K'(3, 2), L'(–1, 1), M'(–4, 1) C.J'(–4, 2), K'(–1, 2), L'(–1, 1), M'(–4, 1) D.J'(6, 2), K'(–1, 2), L'(–1, 1), M'(–4, 1) Find the coordinates of the vertices of rectangle JKLM with vertices J(–5, 4), K(–2, 4), L(–2, 3), and M(–5, 3) translated by (1, –2). (over Chapter 6)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.P'(1, –2), Q'(4, –2), R'(4, –1), S'(1, 2) B.P'(1, –2), Q'(4, –2), R'(4, –1), S'(1, 0) C.P'(1,4), Q'(4, –2), R'(4, –1), S'(1, 0) D.P'(1, –2), Q'(4, 4), R'(4, –1), S'(1, 0) Find the coordinates of the vertices of trapezoid PQRS with vertices P(–4, –3), Q(–1, –3), R(–1, –2), and S(–4, –1) translated by (5, 1). (over Chapter 6)

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1.A 2.B 3.C 4.D Five Minute Check 5 A.40° B.80° C.100° D.140° Refer to the figure. What is the measure of angle C? (over Chapter 6)

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