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Circle Measurements and Formulas

Learn how to find the area, circumference, radius, and diameter of circles using formulas and the value of pi. Practice solving example problems and apply the concepts to real-life scenarios.

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Circle Measurements and Formulas

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  1. Warm up Find each measurement. 1. the height of the parallelogram, in which A = 182x2 mm2 h = 9.1x mm 2. the perimeter of a rectangle in which h = 8 in. and A = 28x in2 P = (16 + 7x) in. 3. the area of the trapezoid A = 16.8x ft2

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

  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. Example 1A: Finding Measurements of Circles 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.

  5. 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.

  6. 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

  7. Example 1C Continued Step 2 Use the value of r to find the circumference. C = 2r C = 2(5x) Substitute 5x for r. C = 10x ft Simplify.

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

  9. Example 2: 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

  10. Lesson Quiz: Part I 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

  11. Lesson Quiz: Part II Find each measurement. 3. 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

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