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Define the radius, diameter, and circumference of a circle.

Warm-Up. Define the radius, diameter, and circumference of a circle. Draw the radius of the circle and a diameter of the circle. Find the area of  K in terms of . Area of a circle. A =  r 2. Divide the diameter by 2 to find the radius, 3. A = (3) 2. A = 9  in 2.

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Define the radius, diameter, and circumference of a circle.

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  1. Warm-Up • Define the radius, diameter, and circumference • of a circle. • Draw the radius of the circle and a diameter of • the circle. Find the area of K in terms of . Area of a circle. A = r2 Divide the diameter by 2 to find the radius, 3. A = (3)2 A = 9 in2 Simplify.

  2. Objectives Develop and apply the formulas for the area and circumference of a circle. Develop and apply the formula for the area of a regular polygon.

  3. The irrational number  is defined as the ratio of the circumference C to the diameter d, or A circleis the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol  and its center. Ahas radius r= ABand diameter d= CD. Solving for C gives the formula C = d. Also d = 2r, so C = 2r.

  4. http://www.mathwarehouse.com/geometry/circle/circumference-of-circle.phphttp://www.mathwarehouse.com/geometry/circle/circumference-of-circle.php http://www.learner.org/courses/learningmath/measurement/session7/part_b/index.html

  5. Example 1: Cooking Application A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth. 24 cm diameter 36 cm diameter 48 cm diameter A = (12)2 A = (18)2 A = (24)2 ≈ 452.4 cm2 ≈ 1017.9 cm2 ≈ 1809.6 cm2

  6. Example 2 Find each measurement. 1. the area of D in terms of  A = 49ft2 2. the circumference of T in which A = 16mm2 C = 8 mm

  7. Example 1B: Finding Measurements of Circles Find the radius of J if the circumference is (65x + 14) m. C = 2r Circumference of a circle (65x + 14) = 2r Substitute (65x + 14) for C. r = (32.5x + 7) m Divide both sides by 2.

  8. Example 1C: Finding Measurements of Circles Find the circumference of M if the area is 25 x2ft2 Step 1 Use the given area to solve for r. A = r2 Area of a circle 25x2 = r2 Substitute 25x2 for A. 25x2 = r2 Divide both sides by . Take the square root of both sides. 5x = r

  9. Helpful Hint The key gives the best possible approximation for on your calculator. Always wait until the last step to round.

  10. Example Find each measurement. Speakers come in diameters of 4 in., 9 in., and 16 in. Find the area of each speaker to the nearest tenth. A1≈ 12.6 in2 ; A2≈ 63.6 in2 ; A3≈ 201.1 in2

  11. Homework • P. 603 (2-5, 10-13, 33, 51, and 52) • Quiz tomorrow over sections 9-1 and 9-2 • Extra Credit: p. 615 (1-9)

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