11.1 NOTES Circumference and Arc Length 1 BELLWORK: What is π ? 3 14159 The ratio of a circle's circumference to its diameter LESSON 11.1 - Circumference and Arc Length • The CIRCUMFERENCE of a circle is the distance around the circle. • For all circles, the ratio of the circumference C to the diameter d is the same. This ratio is = π. • Solving the ratio for C yields the formula for the circumference of a circle. CIRCUMFERENCE OF A CIRCLE C d C = πd OR C =2πr r r d Find the circumference of a circle with a diameter of 12 inches. Round to the nearest tenth. 12 in C = 12 π C ≈ 37 7 in Find the circumference of a circle with a radius of 93 centimeters. Round to the nearest tenth. 93 cm C = 2 π 93 C ≈ 584 3 cm Find the diameter of a circle with a circumference of 62 feet. Round to the nearest tenth. d 62 = d π d ≈ 19 7 ft
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11.1 NOTES - Circumference and Arc Length€¦ · 11.1 NOTES Circumference and Arc Length 3 Find the circumference of C given that mAB = 76° and the length of AB is 14 meters. 14
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11.1 NOTES Circumference and Arc Length
1
BELLWORK: What is π?
3.14159....
The ratio of a circle's circumference to its diameter.
LESSON 11.1 - Circumference and Arc Length
• The CIRCUMFERENCE of a circle is the distance around the circle.
• For all circles, the ratio of the circumference C to the diameter d is the same. This ratio is = π .
• Solving the ratio for C yields the formula for the circumference of a circle.
CIRCUMFERENCE OF A CIRCLE
Cd
C = πdOR
C = 2πr
rr
d
Find the circumference of a circle with a diameter of 12 inches. Round to the nearest tenth.
12 in
C = 12π
C ≈ 37.7 in
Find the circumference of a circle with a radius of 93 centimeters. Round to the nearest tenth.
93 cm
C = 2 π 93
C ≈ 584.3 cm
Find the diameter of a circle with a circumference of 62 feet. Round to the nearest tenth.
d
62 = dπ
d ≈ 19.7 ft
11.1 NOTES Circumference and Arc Length
2
Find the radius of a circle with a circumference of 7 millimeters. Round to the nearest tenth.
r7 = 2 π r
r ≈ 1.1 mm
The measurements of a tire are given below. How many FEET does the tire travel in one revolution? If the tire has traveled 500 feet, how many revolutions did the tire complete?
17 inches
5 inches
5 inches
d = 5 + 17 + 5
d = 27 inches
C = 27πC ≈ 84.8 in
C ≈ 7.1 ft
The tire covers about 7.1 feet in
one revolution
500 = x(27π)x ≈ 5.9 rev.
In order to travel 500 feet, the tire must make almost 6 revolutions (5.9)
• An ARC LENGTH is a portion of the circumference of a circle.
• We can use the measure of an arc (in degrees) to find its length (in linear units, such as centimeters).
ARC LENGTHIn a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°.
C
A
B
Arc length of AB2πr
mAB360°
=
Find the length of arc AB given that the radius is 11 cm and mAB = 64°.
11 cm
64° C
A
B
AB 64°2 π 11 360°
=
AB22π = 0.18
AB = 12.3 cm
Find the length of arc AB given that the radius is 53 ft and mAB = 165°.
53 ft
165°
CA
B
AB 165°2 π 53 360°
=
AB106π = 0.4583
AB = 152.6 ft
Find the length of a radius of C given that mAB = 182° and the length of AB is 63 yards.
63 yd
182° C
A
B63 182°2 π r 360°=
632π r = 0.5056
r = 19.8 yd
10.02r = 0.5056
10.02 = 0.5056r
11.1 NOTES Circumference and Arc Length
3
Find the circumference of C given that mAB = 76° and the length of AB is 14 meters.
14 m
76°C
AB14 76°
2 π r 360°=
142π r = 0.2111
r = 10.6 m
2.23r = 0.2111
2.23 = 0.2111r
Find mAB given that the radius of C is 29 miles and the length of AB is 56 miles.
56 mi
29 miC
A
B
56 m AB2 π 29 360°
=
m AB360°
0.307 =
m AB = 110.6°
Find mAB given that the radius of C is 44 feet and the length of AB is 32 feet.
32 ft
44 ft
C
A
B
32 m AB2 π 44 360°
=
0.116 =
m AB = 41.7°
m AB360°
HOMEWORK:11.1 Worksheet ‑ Circumference and Arc Length