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Objectives: Find the areas of circles, sectors, and segments of circles

Section 7-7 Circles and Sectors SPI 32L: determine the area of indicated regions involving circles SPI 33B: find the area of a sector of a circle given a diagram. Objectives: Find the areas of circles, sectors, and segments of circles. Recall

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Objectives: Find the areas of circles, sectors, and segments of circles

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  1. Section 7-7 Circles and Sectors SPI 32L: determine the area of indicated regions involving circlesSPI 33B: find the area of a sector of a circle given a diagram • Objectives: • Find the areas of circles, sectors, and segments of circles Recall Area of a Circle A = r2

  2. Real-world and Pizza How much more pizza is in a 12 inch diameter pizza than in a 10 inch diameter pizza? 10-inch pizza Radius = 10/2 = 5 Area = (5)2 = 25 12-inch pizza Radius = 12/2 = 6 Area = (6)2 = 36 Difference in Area = 36 - 25 = 11  34.6 in2

  3. Sectors of Circles • Sector of a Circle: • region bounded by an arc of the circle and the two radii to the arcs endpoints • name by using one arc endpoint, the center of the circle, and the other arc endpoint • (AOB of Circle O) A arc radius B O radius

  4. Area and Sectors of Circles • The area of a sector is a fractional part of the area of a circle. • The ratio of a sector’s area to a circle’s area is: • measure of the arc • 360

  5. mAB 360 area of sector ACB = • r2 = • (6)2 100 360 5 18 = • 36 = 10 The area of sector ACB is 10 m2. Areas of Circles and Sectors Find the area of sector ACB. Leave your answer in terms of π . . .

  6. Segments of a Circle • Part of the circle bounded by an arc and the segments joining the arc’s endpoints Segment of a circle

  7. Finding Area of a Segment of a Circle - = - ? =

  8. area of sector AOB = • r2Use the formula for area of a sector. mAB 360 120 360 = • (24)2Substitute. = • 576 = 192 Simplify. 1 3 Areas of Circles and Sectors Find the area of the shaded segment. Round your answer to the nearest tenth. Step 1: Find the area of sector AOB.

  9. You can use a 30°-60°-90° triangle to find the height h of AOB and AB. 24 = 2hhypotenuse = 2 • shorter leg 12 = hDivide each side by 2. = 3 • 12 = 12 3 longer leg = 3• shorter leg AB = 24 3 Multiply each side by 2. AB 2 AOB has base 12 3 ft + 12 3 ft, or 24 3 ft and height 12 ft. 1 2 A = bh Area of a triangle A = (24 3 )(12) Substitute 24 for b and 12 for h. A = 144 3 Simplify. 1 2 (continued) Step 2: Find the area of AOB.

  10. Step 3: Subtract the area of AOB from the area of sector AOB to find the area of the segment of the circle. area of segment = 192 – 144 3 353.77047 Use a calculator. (continued) To the nearest tenth, the area of the shaded segment is 353.8 ft2.

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