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
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
Find the EXACT circumference.
28 ft1.r = 14 feet
2.d = 15 miles
15 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 arc
Arc Length 2360
r
Ex 6. Find the Arc LengthRound to the nearest hundredths
8m
70
9.77 m
measure of arc
Arc Length 2360
r
Ex 7. Find the Arc Length Round to the nearest hundredths
12 in
110
23.04 in
measure of arc
Arc Length 2360
r
Ex 8. Find the exact Arc Length.
10 in
3
measure of arc
Arc Length 2360
r
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
ClassworkPractice from Notes Page
AreaThe amount of space occupied.
r A= pr2
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
Another Example!
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 arc
360A r
Example Find the area of the sector to the nearest hundredths.
A 18.85 cm2
606 cm
Q
R
Example Find the exact area of the sector.
6 cm
120
7 cm
Q
R
249A cm
3
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
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
Homework9 Problems
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