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Warm Up

Areas of Circles and Sectors. Warm Up. Lesson Presentation. Lesson Quiz. about 201.06 cm 2. ANSWER. 1. 2. Radius:. mi. 1. 3. about 5.59 mi 2. ANSWER. Warm-Up. Find the area of a circle with the given measure. 1. Radius: 8 cm. 4 π ft 2. ANSWER. 100. 4. Solve x 2 =. π. _.

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Warm Up

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  1. Areas of Circles and Sectors Warm Up Lesson Presentation Lesson Quiz

  2. about 201.06 cm2 ANSWER 1 2. Radius: mi 1 3 about 5.59 mi2 ANSWER Warm-Up Find the area of a circle with the given measure. 1. Radius: 8 cm

  3. 4π ft2 ANSWER 100 . 4. Solvex2 = π _ + 5.64 about ANSWER Warm-Up Find the area of a circle with the given measure. 3. Circumference: 4π ft

  4. = π (2.5)2 The area of A is about 19.63 square centimeters. Example 1 Find the indicated measure. a. Area r= 2.5 cm SOLUTION A = πr2 Write formula for the area of a circle. Substitute 2.5 for r. = 6.25π Simplify. ≈ 19.63 Use a calculator.

  5. 113.1 = r2 π Example 1 Find the indicated measure. b. Diameter A = 113.1 cm2 SOLUTION A = πr2 Write formula for the area of a circle. 113.1 = πr2 Substitute 113.1 for A. Divide each side by π. 6 ≈ r Find the positive square root of each side. The radius is about 6 cm, so the diameter is about 12 cm.

  6. Find the areas of the sectors formed by UTV. STEP 1 Find the measures of the minor and major arcs. Because m UTV = 70°, mUV = 70° and mUSV = 360° – 70° = 290°. Example 2 SOLUTION

  7. Find the areas of the small and large sectors. STEP 2 290° = π 82 360° mUV Area of small sector = πr2 360° 70° = π 82 360° mUSV Area of large sector = πr2 360° Example 2 Write formula for area of a sector. Substitute. ≈ 39.10 Use a calculator. Write formula for area of a sector. Substitute. ≈ 161.97 Use a calculator. The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively.

  8. 1. Area of D ANSWER about 615.75 ft2 ANSWER about 205.25 ft2 ANSWER about 410.50 ft2. Guided Practice Use the diagram to find the indicated measure. 2. Area of red sector 3. Area of blue sector

  9. 315 = Area ofV Solve for Area of V. The area of Vis 315 square meters. mTU Area of sectorTVU = Area ofV 360° 40° 35 = Area ofV 360° Example 3 Use the diagram to find the area of V. SOLUTION Write formula for area of a sector. Substitute.

  10. Example 4 SOLUTION The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.

  11. 180° = 36(26) – (π 82 ) + 162 360° ANSWER The correct answer is C. Example 4 = 936 – [32π+ 256] ≈ 579.47 The area is about 579square feet.

  12. 4. Find the area of H. ANSWER about 907.92 cm2 Guided Practice

  13. 5. Find the area of the figure. ANSWER about 43.74 m2 Guided Practice

  14. ANSWER Yes; the formula for the area of sector is m π r2 A= and if you solve this for m, you get 360 360A . π r2 Guided Practice 6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain.

  15. ANSWER 106.03 in.2, 148.44 in.2 Lesson Quiz 1. Find the area of the sectors formed by DEF.

  16. 2. Use the area of the sector to find the area of R ANSWER 211.09 cm2 Lesson Quiz

  17. 3. Find the area of the shaded region. ANSWER 23.18ft2 Lesson Quiz

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