Central Angles and Arc Length in a Circle Using Proportions

What is the formula to calculate the arc length of a circle?

• Arc Length = πr(θ/180)

• Arc Length = 2πr(θ/360)

• Arc Length = r(θ/360)

• Arc Length = 2πr(θ/180)

How is the area of a sector of a circle calculated when θ is in degrees?

• Area of Sector = θ/360 * πr

• Area of Sector = θ/180 * πr^2

• Area of Sector = θ/360 * πr^2

• Area of Sector = 2πr(θ/360)

Lin thinks that the central angle in circle A is congruent to the central angle in circle B. Do you agree with Lin? Show or explain your reasoning.

• I agree. The ratios of the arc length to the radius are equivalent.

• I disagree. The ratios of the arc length to radius are not equivalent.

What is the arc length of minor arc AB?

• 5.23

• 103

• 33.33

• 50

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

Find the arc length of arc AB.

• 12.57 units

• 75.40 units

• 24 units

• 125.66 units

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40

• 35

• 55

• 69

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

FIND THE ARC LENGTH OF THE BOLDED ARC

• A

• B

• C

• D

Lin thinks that the central angle in circle A is congruent to the central angle in circle B. Do you agree with Lin? Show or explain your reasoning.

• I agree. The ratios of the arc length to the radius are equivalent.

• I disagree. The ratios of the arc length to radius are not equivalent.