Understanding Arc Length of a Circle

Mr. Brown explains how to find the arc length of a circle, which is a portion of the circle's circumference. He introduces two formulas: one for angles in degrees and another for radians. The video includes three examples: calculating arc length with a given radius and angle, finding the radius from arc length and angle, and determining the perimeter of a shaded region in a circle. Mr. Brown emphasizes the importance of using the correct units and understanding the difference between arc length and arc measure.

What is the arc length of a circle?

• The diameter of the circle

• The entire circumference of the circle

• A portion of the circle's circumference

• The radius of the circle

Which of the following is NOT needed to calculate the arc length?

• Radius

• Circumference

• Central angle

• Diameter

What is the formula for arc length when the angle is in degrees?

• Theta times 2πR

• Theta divided by 180 times πR

• Theta times R

• Theta divided by 360 times 2πR

In the first example, what is the approximate arc length for a radius of 2.5 cm and an angle of 95 degrees?

• 3.14 cm

• 4.15 cm

• 5.25 cm

• 6.28 cm

What is the exact arc length in the first example?

• 72/95

• 72π/95

• 95/72

• 95π/72

In the second example, what is the radius if the arc length is 50 units and the central angle is 120 degrees?

• 30.1 units

• 20.5 units

• 23.9 units

• 25.7 units

What is the formula used to find the radius in the second example?

• Arc length divided by (Theta/360) times 2π

• Arc length times (Theta/180) divided by π

• Arc length divided by (Theta/180) times π

• Arc length times (Theta/360) divided by 2π

In the third example, what is the central angle of the shaded region if the given angle is 80 degrees?

• 100 degrees

• 360 degrees

• 280 degrees

• 180 degrees

What additional components are needed to calculate the perimeter of the shaded region in the third example?

• Only the central angle

• Only the arc length

• The radii of the circle

• The diameter of the circle

What is the total perimeter of the shaded region in the third example?

• 48.9 units

• 78.9 units

• 68.9 units

• 58.9 units