Warm up: Solve for x

18◦

1.)

x

124◦70◦

x

2.)

3.)

x

260◦

20◦110◦ x

4.)

53 145

8070

Questions over hw?

Daily Check

Circumference & Arc Length

of Circles

CircumferenceThe distance around a circle

orC 2 r

C d

Circumference

Find the EXACT circumference.

28 ft1.r = 14 feet

2.d = 15 miles15 miles

Ex 3 and 4: Find the circumference. Round to the nearest tenths.

89.8 mm 103.7 yd

5. A circular flower garden has a radius of 3 feet. Find the circumference of the garden to the nearest hundredths.

C = 18.85 ft

r2 C C 2 3

Arc LengthThe distance along the curved line

making the arc (NOT a degree amount)

Arc Length

measure of arcArc Length 2

360r

Ex 6. Find the Arc LengthRound to the nearest hundredths

8m

70

9.77 m

measure of arcArc Length 2

360r

Ex 7. Find the Arc Length Round to the nearest hundredths

12 in

110

23.04 in

measure of arcArc Length 2

360r

Ex 8. Find the exact Arc Length.

10 in3

measure of arcArc Length 2

360r

Ex 9. What happens to the arc length if the radius were to be doubled? Halved?

20 5 in, in3 3

measure of arcArc Length 2

360r

ClassworkPractice from Notes Page

2 Types of Answers

Rounded• Type the Pi

button on your calculator

• Toggle your answer

• Do NOT write Pi in your answer

Exact• Pi will be

in your answer

AreaThe amount of space occupied.

r A= r2

Find the EXACT area.

2841 ft1.r = 29 feet

2.d = 44 miles2484 mi

Find the area. Round to the nearest tenths.

2181.5 yd 22206.2 cm

Example 3

If S has a diameter of 10 inches, find the area of the circle to the nearest hundredths.

A = 78.54 in2

Sectorthe region bounded by two radii of the

circle and their intercepted arc.

Area of a Sector

2measure of arc360

A r

Example 4 Find the area of the sector to the nearest hundredths.

A 18.85 cm2

606 cm

Q

R

Example 5 Find the exact area of the sector.

6 cm

120

7 cm

Q

R

249A cm3

Example 6

Find the area of a sector with a central angle of 45° if the diameter of the circle is 12 inches. Round to the nearest hundredths. A 14.14 in2

Example 7 A spinner is divided into 12 equal sections and the radius of the spinner is 4 inches. Every other section is shaded. Find the exact total area of the shaded region on the spinner.

A = 8 in2

Homework9 Problems