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Areas of Circles and Sectors

Areas of Circles and Sectors. Thursday, September 11, 2014. How do we find the areas of circles and sectors?. Lesson 6.8. M2 Unit 3: Day 10. 2. Radius. 1. Circumference. C = 48 ft. about 7.64 ft. ANSWER. ANSWER. about 81.68 in. Daily Homework Quiz. Warm-Up.

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Areas of Circles and Sectors

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  1. Areas of Circles and Sectors Thursday, September 11, 2014 How do we find the areas of circles and sectors? Lesson 6.8 M2 Unit 3: Day 10

  2. 2. Radius 1. Circumference C = 48 ft about 7.64 ft ANSWER ANSWER about 81.68 in. Daily Homework Quiz Warm-Up Find the indicated measure.

  3. 4. Find the total circumference of the circles. 3. Length of AB ANSWER 8.64 cm ANSWER 100.53 cm Daily Homework Quiz Warm-Up

  4. 6. Circumference 5. Radius about 222.72 in. ANSWER ANSWER about 21.88 cm Daily Homework Quiz Warm-Up Find the indicated measure.

  5. Homework Warm-Up # 22 P.227 Show your work below. Use your own paper

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

  7. b. Diameter 113.1 = r2 π A = 113.1 cm2 ANSWER The radius is about 6 centimeters, so the diameter is about 12 centimeters. EXAMPLE 1 EXAMPLE Use the formula for area of a circle Find the indicated measure. 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.

  8. Sector of a Circle:the region bounded by two radii of the circle and their intercepted arc

  9. Area of a Sector: a portion of the area of the whole circle S

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

  11. Find the areas of the sectors formed by UTV. mUV Area of small sector = πr2 360° 70° = π 82 360° EXAMPLE 2 EXAMPLE Find areas of sectors STEP 2 Find the areas of the small and large sectors. Write formula for area of a sector. Substitute. ≈ 39.10 Use a calculator.

  12. 290° = π 82 360° ANSWER The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively. mUSV Area of large sector = πr2 360° EXAMPLE 2 EXAMPLE Find areas of sectors Write formula for area of a sector. Substitute. ≈ 161.97 Use a calculator.

  13. 1. Area of D = π (14)2 The area of Dis about 615.75 ft2. GUIDED PRACTICE Guided Practice Use the diagram to find the indicated measure. SOLUTION A = πr2 Write formula for the area of a circle. Substitute 14 for r. = 196π Simplify. = 615.75 Use a calculator

  14. Because m FDE = 120, mFE = 120 and mFGE = 360 – 120 = 240. GUIDED PRACTICE Guided Practice Use the diagram to find the indicated measure. 2. Area of red sector SOLUTION STEP 1 Find the measures of major arcs.

  15. mFE Area of red sector = π r2 360 120 = π 142 360 ANSWER The area of red sector is about 205.25 ft2. GUIDED PRACTICE Guided Practice STEP 2 Find the area of red sector. Write formula for area of a sector. Substitute. = 205.25 Use a calculator.

  16. Because m FDE = 120, MFE = 120 and mFGE = 360 – 120 = 240. GUIDED PRACTICE Guided Practice Use the diagram to find the indicated measure. 3. Area of blue sector SOLUTION STEP 1 Find the measure of the blue arc.

  17. mFEG Area of blue sector = π r2 360 240 = π 142 360 ANSWER Area of blue sector is about 410.50 ft2. Guided Practice STEP 2 Find the area of blue sector. Write formula for area of a sector. Substitute. = 410.50 ft2 Use a calculator.

  18. 315 = Area of V Solve for Area of V. The area of V is 315 square meters. mTU Area of sector TVU = Area of V 360° 40° 35 = Area of V ANSWER 360° EXAMPLE Use the Area of a Sector Theorem Use the diagram to find the area of V. SOLUTION Write formula for area of a sector. Substitute.

  19. EXAMPLE 4 Standardized Test Practice 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.

  20. 180° = 36(26) – (π 82 ) + 162 360° ANSWER The correct answer is C. EXAMPLE 4 Standardized Test Practice = 936 – [32π+ 256] ≈ 579.47 The area is about 579square feet.

  21. 4. Find the area of H. 907.92 = Area of H Solve for Area of H. ANSWER The area of H is 907.92 cm2. mFG Area of sector FHG = Area of H 360 85 214.37 = Area of H 360 GUIDED PRACTICE Guided Practice SOLUTION Write formula for area of a sector. Substitute.

  22. 1 A = b h 2 1 = 7 7 2 GUIDED PRACTICE Guided Practice 5. Find the area of the figure. SOLUTION Take the topas base, which is 7 m and find the area of the triangle STEP 1 Write formula for area of a triangle. Substitute. = 24.5 = 24.5 m

  23. 1 A = π r2 2 ANSWER 1 = π (3.5)2 The area of the figure is about 43.74 m2. 2 GUIDED PRACTICE Guided Practice STEP 2 find the area of the semicircle Write formula for area of a sector. Substitute. = 19.5 multiply STEP 3 Add the areas Area of figure = Area of triangle + Area of semicircle = 24.5 + 19.5 = 43.74 m2

  24. m π r2 A= and if you solve this for m, you get 360 360A π r2 GUIDED PRACTICE 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. SOLUTION yes; the formula for the area of sector is

  25. Homework: Page 232 (#1-15 all)

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