Geometry Arc Lengths and Areas of Sectors Arc

Geometry Arc Lengths and Areas of Sectors

Arc Length n 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.

Sector of a circle n A region bounded by 2 radii and an arc. .

Portions of a Circle: Determine the Arc measure based on the portion given. 180 o 90 o 120 o 180 o 60 o 120 o 60 o A. B. C. D. ¼ of a circle: ¼ ● 360 ½ of a circle: ½ ● 360 1/3 of circumference : 6π out of a total 36π on the circle: 1/3 ● 360 1/6 ● 360

Area of a Sector Formula measure of the central angle or arc Area of a sector = m 2 πr 360 The area of the entire circle! The fraction of the circle! .

Arc Length Formula measure of the central angle or arc m 2πr 360 The circumference of the entire circle! Arc Length = The fraction of the circle! .

Find the length of AB and the area of sector AOB. 1. A 90 o O 90 o 6 2. 240 o 3. 240 o B O 12 A 300 o 12 Length of AB ¼ Fraction ● circumference ¼ ● 12π 3π units Area of sector AOB Fraction ● area A O O 120 o 2. 4 5. A B 108 o O 10√ 2 B B Fraction of circle: 120 o 4. B Fraction of circle: 2/3 5/6 1/3 Length of AB Fraction ● circumference Length of AB 2/3 ● 24π 16π units 5/6 ● 24π 20π units Area of sector AOB Fraction ● area Length of AB Fraction ● circumference 1/3 ● 4. 8π 1. 6π units Area of sector AOB Fraction ● area Fraction of circle: 3/10 Length of AB 3/10 ● 20√ 2π 6√ 2π units Area of sector AOB Fraction ● area ¼ ● 36π 2/3 ● 144π 5/6 ● 144π 1/3 ● 5. 76π 3/10 ● 200π 9π units 2 96π units 2 120π units 2 1. 92π units 2 60π units 2 A

6. The area of sector AOB is 48π and Area of a sector = m πr 2 360 270 48π = πr 2 360 4 16 3 2 4 48 = r 3 4 3 64 = r 2 r=8 . Find the radius of ○O.

7. The area of sector AOB is Area of a sector = and m πr 2 360 9 40 π= πr 2 4 360 99 1 2 9 = r 1 4 9 1 81 2 = r 4 r= 9 2 . Find the radius of ○O.

Find the area of the shaded region. Point O marks the center of the circle. 8. 9. 11. 10. 60˚ 8 160 3 π units 2 12 O 6 9π - 18 units 2 O 30 60 24π - 36√ 3 units 2 O 4 8π - 8√ 3 units 2

HW Khan academy n Due Tuesday march 6 th at 8 am n Quiz Tuesday/Wednesday over arc length and sector area n

Some common fractions and measures! Arc or Central Angle Measure Fraction of the Circle 36 o 1/10 108 o 3/10 60 o 1/6 300 o 5/6 120 o 1/3 240 o 2/3 30 o 1/12 330 o 11/12 45 o 1/8 225 o 5/8