Calculating Arc Length and Sector Area of Circles

Mr. Allen explains how to calculate arc length and sector area of a circle using proportions. He demonstrates the process with a circle of radius 10 inches and a central angle of 140 degrees. The video covers the formulas for arc length and sector area, emphasizing the use of proportions to solve for unknowns. Mr. Allen provides both exact and approximate solutions, highlighting the importance of understanding when to use each. The video concludes with practical applications and tips for math tests.

What is the radius of the circle discussed in the video?

• 14 inches

• 140 degrees

• 360 degrees

• 10 inches

What is the central angle of the circle mentioned?

• 180 degrees

• 140 degrees

• 360 degrees

• 100 degrees

What proportion is used to find the arc length?

• Arc length/360 = Arc measure/Circumference

• Arc measure/360 = Arc length/Circumference

• Arc measure/360 = Circumference/Arc length

• Arc length/Arc measure = 360/Circumference

How is the circumference of the circle calculated?

• 2 * pi * radius

• pi * diameter

• radius^2 * pi

• Both A and B

What is the exact arc length found in the video?

• 14 pi inches

• 36 pi inches

• 280 pi inches

• 70/9 pi inches

What is the approximate arc length in decimal form?

• 70.9 inches

• 14 inches

• 280 inches

• 24.43 inches

What proportion is used to find the sector area?

• Sector area/Arc measure = 360/Area of circle

• Arc measure/360 = Sector area/Area of circle

• Sector area/360 = Arc measure/Area of circle

• Arc measure/360 = Area of circle/Sector area

How is the area of the circle calculated?

• radius * pi

• 2 * pi * radius

• pi * diameter

• radius^2 * pi

What is the exact sector area found in the video?

• 36 pi inches squared

• 100 pi inches squared

• 1400 pi inches squared

• 350/9 pi inches squared

What is the approximate sector area in decimal form?

• 122.17 inches squared

• 350.9 inches squared

• 100 inches squared

• 1400 inches squared