Bell Ringer 1. What is the proportion to determine arc length?

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Bell Ringer 11-20-18 1. What is the proportion to determine arc length? 2. What is the difference between arc length and arc measure? 3. How do you find the area of a circle?

Area of a Sector Tuesday, November 20, 2018

What is a sector? A sector is a portion of a circle… like a slice of pizza is a portion of the whole pie.

How do we find the Area of a Sector? Since a sector is a portion of a circle, its area is a portion of the entire area of the circle. As stated yesterday, circles are proportional. Yesterday we learned: 𝑨𝒓𝒄 𝑴𝒆𝒂𝒔𝒖𝒓𝒆 360° = 𝑨𝑟𝑐 𝑳𝑒𝑛𝑔𝑡ℎ 𝑪𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 Today we extend that to the area of a circle: 𝐴𝑟𝑐 𝑀𝑒𝑎𝑠𝑢𝑟𝑒 360° = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑆𝑒𝑐𝑡𝑜𝑟 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝐶𝑖𝑟𝑐𝑙𝑒 AND/OR 𝐴𝑟𝑐 𝐿𝑒𝑛𝑔𝑡ℎ 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑨𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑺𝑒𝑐𝑡𝑜𝑟 𝑨𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑪𝑖𝑟𝑐𝑙𝑒

Remember your formulas… Circumference: C = 2𝜋𝑟 C = 𝜋𝑑 Area: 𝐴=𝜋 𝑟 2

Examples Find the area of a sector: 1. Radius 4 ft, arc measure 80º 2. Radius 9 in, central angle 60º 3. Central angle 98º, arc length 8.2 cm 4. Central angle 138º, arc length 24.6 ft Find the radius of a circle: 5. Sector area 59 in2, central angle 40º 6. Sector area 8 in2, central angle 72º

Classwork Geometry book p. 695-696 #3-33 odd Homework Area of a Sector

Remember… in circles things are proportional. Exit Ticket 1. How do you find the area of a sector given radius and arc measure? 2. How do you find the area of a sector given central angle and arc length? 3. How do you find the radius of a circle given area of the sector and central angle?