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## CIRCLES

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**Geometry**Lessons 8.5 and 8.6 Area of Circles, Sectors and Segments HW: 8.5/1-8, 12-14 8.6/1-12**Circumference**3in C ≈ 18.8in**πr**r**Finding the area given the diameter**d r = 2 The radius of a circle is half of its diameter, or We can substitute this into the formula A = πr2**How to find the area of a circle given the radius**Find the area of the circle below: Substitute the values for p and r.**How to find the area of a circle**given the diameter Given the diameter: Radius = diameter divided by 2 Substitute the values for p and r.**How would you find the shaded area?**Find the area of the square and subtract the area of the circle.**The area of a circle**2 cm 10 m 78 cm 23 mm Use π = 3.14 to find the area of the following circles: A = πr2 A = πr2 = 3.14 × 22 = 3.14 × 52 = 12.56 cm2 = 78.5 m2 A = πr2 A = πr2 = 3.14 × 232 = 3.14 × 392 = 1661.06 mm2 = 4775.94 cm2**Find the area of this shape**Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. Area of circle = 3.14 × 6.52 13 cm 6 cm = 132.665 cm2 Area of rectangle = 6 × 13 = 78 cm2 Total area = 132.665 + 78 = 210.665 cm2**The circumference of a circle is 18. Find the area of**the circle, leave answer in terms of . C = 2 r A = r2 A = 92 A = 81 18 = 2r 9 = r**Arc Length Reminder**• The length of part of the circumference. The length of the arc depends on what two things? 1) The measure of the arc. 2) The size of the circle. An arc length measures distance while the measure of an arc is in degrees.**Arc Length Formula**measure of the central angle or arc m The circumference of the entire circle! 2πr Arc Length = 360 The fraction of the circle! .**REVIEW: Finding Arc Length**Find the arc length. Give answers in terms of and rounded to the nearest hundredth. FG Use formula for area of sector. Substitute 8 for r and 134 for m. Simplify. 5.96 cm 18.71 cm**Sectors**Let’s talk pizza**Sector of a circle**• A region bounded by 2 radii and their intercepted arc. .**Area of a Sector Formula**measure of the central angle or arc m˚ πr2 Area of a sector = 360 The area of the entire circle! The fraction of the circle! .**Finding the Area of a Sector**Find the area of the sector. Give answers in terms of and rounded to the nearest hundredth. sector HGJ Use formula for area of sector. Substitute 12 for r and 131 for m. = 52.4 m2 164.54 m2 Simplify.**Finding the Area of a Sector**Find the area of the sector. Give answers in terms of and rounded to the nearest hundredth. sector ABC Use formula for area of sector. Substitute 5 for r and 25 for m. Simplify. 1.74 ft2 5.45 ft2**The area of sector AOB is**and Find the radius of ○O. m Area of a sector = πr2 360 9 40 π = πr2 4 360 9 9 9 1 = r2 1 1 4 9 81 = r2 4 9 r = 2**The area of sector AOB is 48π and**Find the radius of ○O. m πr2 Area of a sector = 360 270 48π = πr2 360 A O 4 16 4 3 r2 48 = 3 4 3 r2 64 = = 8 r B**Finding the Area of a Sector**Find the area of each sector. Give your answer in terms of and rounded to the nearest hundredth. sector JKL Use formula for area of sector. Substitute 16 for r and 36 for m. = 25.6 in2 80.42 in2 Simplify.**Automobile Application**A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 122°? Use formula for area of sector. r = 18 in. m˚ = 122˚ Simplify. 345 in2**AREA OF SEGMENT**A segment of a circle is a region bounded by an arc and its chord.**= ¼100π= 25π**=½∙10∙10=50 10 Area of Segment = 25π - 50**Check It Out!**Find the area of segment RST to the nearest hundredth. Step 1 Find the area of sector RST. Use formula for area of sector. Substitute 4 for r and 90 for m. Simplify. = 4 m2**Check It Out! Continued**Find the area of segment RST to the nearest hundredth. Step 2 Find the area of ∆RST. ST = 4 m, and RS = 4m. Simplify. = 8 m2**Check It Out! Continued**Find the area of segment RST to the nearest hundredth. Step 3 area of segment = area of sector RST – area of ∆RST = 4 – 8 4.57 m2**Lesson Quiz: Part I**Find each measure. Give answers in terms of and rounded to the nearest hundredth. 1. area of sector LQM 7.5in223.56 in2 2. length of NP 2.5 in. 7.85 in.**Lesson Quiz: Part II**3. The gear of a grandfather clock has a radius of 3 in. To the nearest tenth of an inch, what distance does the gear cover when it rotates through an angle of 88°? 4.6 in. 4. Find the area of segment GHJ to the nearest hundredth. 55.94 m2**60˚**8 12 6 30 4 60 8. 9. 10. 11. O O O 160 9π - 18 units2 24π - 36√3 units2 8π - 8√3 units2 π units2 3**Some common fractions and measures!**3/10 1/10 60o 300o 240o 1/3 1/12 330o 45o 225o