Do Now Agenda Homework Handout (10 problems)  Do Do Now! 12/5: Use formulas to find circumference & area of circles and use proportions to find arc length & sector area of circles. Do Now On your desk: - Pencil & Calculator - Today’s handouts Do Do Now! Agenda Do Now! Guided Practice Independent Practice Exit Ticket Homework Handout (10 problems) 

We will learn to… Use formulas to find circumference & area of circles.

Circle: Circumference: C = d or C = 2r Area: A = r2 NOTE: • Distance around the edge of a circle Formula: C = d or C = 2r Area: • the size of a surface Formula: NOTE: A = r2 Radius is half the diameter. -- OR – Diameter is double the radius.

EXAMPLE 1 Use the formula for circumference Round to the nearest hundredth if necessary. a. Find the circumference of a circle with a radius of 9 cm SOLUTION 56.55 cm ANSWER C = 2πr = 2π(9) = 18π ≈ 56.55

EXAMPLE 1 Use the formula for circumference Round to the nearest hundredth if necessary. b. Find the radius of a circle with a circumference of 26 m SOLUTION 4.14 m ANSWER C = 2πr = 2πr 26 2π 2π 26 2π = r = r 13/π 4.14 ≈ r

Use the formula for area of a circle EXAMPLE 2 Use the formula for area of a circle Round to the nearest hundredth if necessary. a. Find the area of the figure below if its radius is 2.5 cm SOLUTION 19.63 cm2 ANSWER A = πr2 = π(2.5)2 = 6.25π ≈ 19.63

EXAMPLE 2 Use the formula for area of a circle Round to the nearest hundredth if necessary. b. Find the diameter of the CD if its area is 113.1 cm2. SOLUTION d = 12 cm ANSWER A = πr2 113.1 = πr2 π π = r2 113.1 π = r2 36 6 ≈ r

We will learn to… Use proportions to find arc length & sector area of circles.

part of the circumference Sector: Part of area (piece of circle) Arc: part of the circumference Sector: Part of area (piece of circle) Arc Length Arc Length  Sector Area  = = Circumference 360° Area of Circle 360° Arc Length = (θ/360°) * 2πr Sector Area = (θ/360°) * πr2

Find arc lengths and related measures EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. a. Find the arc length of AB SOLUTION Arc Length Circumference 360° =  C = 2(8) ≈ 50.27 cm x 50.27 360° = 60° 360x = 3015.93 Arc length ≈ 8.38 cm

Find arc lengths and related measures EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. b. Find the circumference. SOLUTION Arc Length Circumference 360° =  4.19 C 360° 40° = 40C = 1508.4 C = 37.71 in.

Find arc lengths and related measures EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. c. Find the mRTS. SOLUTION Arc Length Circumference 360° =  C = 2(15.28) ≈ 96 m 44 96 x 360° = 15840 = 96x mRTS = 165°

Find sector areas and related measures EXAMPLE 4 Find sector areas and related measures Round to nearest hundredth if necessary. a. Find the area of small sector SOLUTION Sector Area Area of Circle 360° =  A = (8)² ≈ 201.06 units A 201.06 70° 360° = 360A = 14074.34 A ≈ 39.10 units2

Find sector areas and related measures EXAMPLE 4 Find sector areas and related measures Round to nearest hundredth if necessary. b. Find the area of circle SOLUTION Sector Area Area of Circle 360° =  35 A 360° 40° = 40A = 12600 A = 315 m2

You turn  Complete practice problems 1-8 on your handout First five minutes on your own (in silence)

Answers to Practice C ≈ 15.71 in. 5. Area ≈ 615.75 ft.2 diameter ≈ 5.41 ft. 6. Area ≈ 205.25 ft.2 Arc length ≈ 5.89 yd 7. Area ≈ 410.50 ft.2 C = 81.68 m 8. Area = 907.92 cm2

part of the circumference Sector: piece of the circle Arc: part of the circumference Sector: piece of the circle Arc Length Arc Length  Sector Area  = = Circumference 360° Area of Circle 360°