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Warm up: Solve for x 18 ◦ 1. ) x 124 ◦ 70 ◦ x 2. ) 3. ) x 260 ◦ 20 ◦ 110 ◦ x 4. ) 53 145 80 70

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Page 1: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Warm up: Solve for x

18◦

1.)

x

124◦

70◦

x

2.)

3.)

x

260◦

20◦110◦ x

4.)

53 145

8070

Page 2: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Questions over hw?

Page 3: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Daily Check

Page 4: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Circumference & Arc Length

of Circles

Page 5: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

CircumferenceThe distance around a circle

Page 6: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

orC 2 r

C d

Circumference

Page 7: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

Page 8: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Find the EXACT circumference.

28 ft1.r = 14 feet

2.d = 15 miles

15 miles

Page 9: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

89.8 mm 103.7 yd

Page 10: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

Page 11: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Arc LengthThe distance along the curved line

making the arc (NOT a degree amount)

Page 12: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Arc Length

measure of arc

Arc Length 2360

r

Page 13: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Ex 6. Find the Arc LengthRound to the nearest hundredths

8m

70

9.77 m

measure of arc

Arc Length 2360

r

Page 14: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

12 in

110

23.04 in

measure of arc

Arc Length 2360

r

Page 15: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Ex 8. Find the exact Arc Length.

10 in

3

measure of arc

Arc Length 2360

r

Page 16: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

20 5 in, in

3 3

measure of arc

Arc Length 2360

r

Page 17: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

ClassworkPractice from Notes Page

Page 18: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)
Page 19: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

AreaThe amount of space occupied.

r A= pr2

Page 20: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Find the EXACT area.

2841 ft1.r = 29 feet

2.d = 44 miles2484 mi

Page 21: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Find the area. Round to the nearest tenths.

2181.5 yd 22206.2 cm

Page 22: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Another Example!

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

A = 78.54 in2

Page 23: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Sectorthe region bounded by two radii of the

circle and their intercepted arc.

Page 24: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Area of a Sector

2measure of arc

360A r

Page 25: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

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

A 18.85 cm2

606 cm

Q

R

Page 26: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Example Find the exact area of the sector.

6 cm

120

7 cm

Q

R

249A cm

3

Page 27: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Example

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

Page 28: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Example 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

Page 29: Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Homework9 Problems


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