Exploring Arc Length and Sector Area

This video tutorial covers the concepts of arc length and sector area in circles, revisiting some ideas from the circle unit. It explains how to calculate these using both degrees and radians, providing formulas and examples. The tutorial starts with a review of the circumference of a circle, then moves on to arc length calculations in both degrees and radians. It also covers sector area calculations, again using both degrees and radians, and provides practice problems to reinforce the concepts.

What is the formula for the circumference of a circle?

• C = 2πr

• C = πd

• C = r^2π

• C = 2r

If the central angle is 100 degrees and the radius is 7, what is the arc length?

• 100π/360

• 14π

• 35π/9

• 7π/2

How do you calculate arc length in degrees?

• (Central angle / 180) * Radius

• (Central angle / 360) * Circumference

• 2π * (Central angle / 360)

• π * Radius^2 * (Central angle / 360)

What is the radians formula for arc length?

• (Radius^2) * π * (Central angle / 2π)

• 2π * Radius * (Central angle / 360)

• Radius * Central angle

• π * Radius * Central angle

Given a central angle of 3π/4 radians and a radius of 2, what is the arc length?

• 3π/2

• 6π/4

• π

• 2π/3

How is sector area calculated in degrees?

• (Central angle / 360) * Area of circle

• 2π * Radius * (Central angle / 360)

• π * Radius^2 * (Central angle / 360)

• (Central angle / 180) * π * Radius

For a sector with a central angle of 70 degrees and radius 5, what is the sector area?

• 70π/360

• 25π

• 5π/2

• 175π/36

What is the formula for sector area in radians?

• (Radius^2) * π * (Central angle / 360)

• Radius * Central angle

• π * Radius * (Central angle / 2π)

• (1/2) * Radius^2 * Central angle

If a sector's central angle is 5π/6 radians and its radius is 4, what is the sector area?

• 40π/6

• 20π/3

• 10π/3

• 16π/3

When calculating the arc length for a central angle of 108 degrees and radius 3, what is the result?

• 9π/5

• 18π/5

• 108π/360

• 3π