Understanding Arc Length

The video tutorial explains the concept of arc length, distinguishing it from arc measure. It introduces the formula for calculating arc length using the central angle and circumference. Two examples are provided: one using radius and angle, and another using diameter and angle, to demonstrate the calculation process. The tutorial emphasizes keeping results in terms of Pi for exact lengths.

What is the difference between arc measure and arc length?

• Arc measure is related to the central angle, while arc length is a part of the circumference.

• Arc measure and arc length are the same.

• Arc measure is always in degrees, while arc length is always in radians.

• Arc measure is the length of the arc, while arc length is the angle.

Which of the following is used to calculate the arc length?

• The central angle and the circumference

• The diameter of the circle only

• The radius of the circle only

• The area of the circle

In the formula for arc length, what does '2πr' represent?

• The area of the circle

• The radius of the circle

• The diameter of the circle

• The circumference of the circle

If a circle has a radius of 5 and an angle of 50°, what is the arc length?

• 25π/18 inches

• 50π/36 inches

• 5π inches

• 10π inches

How do you simplify the fraction 50/360 in the context of arc length calculation?

• 10/72

• 5/36

• 1/6

• 25/180

What is the circumference of a circle with a diameter of 34?

• 68π

• 17π

• 170π

• 34π

For a circle with a diameter of 34 and an angle of 150°, what is the arc length?

• 150π/360 cm

• 34π cm

• 85π/6 cm

• 170π/12 cm

What is the first step in calculating the arc length when given the diameter?

• Calculate the circumference

• Convert the angle to radians

• Find the radius

• Determine the central angle

What should you do if asked for the exact arc length?

• Round to the nearest whole number

• Express the length in terms of π

• Use decimals for precision

• Convert to radians

What is the final step in the arc length calculation process?

• Add the radius to the diameter

• Divide the circumference by the central angle

• Multiply the circumference by the central angle

• Multiply the fraction of the circle by the circumference