Calculating Area of a Sector and Arc Length

This video tutorial explains how to calculate the area of a sector and the length of an arc in a circle. It begins with a recap of key terms and introduces formulas for these calculations. The video emphasizes understanding the concept of sectors and arcs as fractions of a circle, using examples with simple and complex angles. It concludes with a practical example problem to demonstrate the application of the formulas.

What is the term used to describe a slice of a circle?

• Radius

• Segment

• Sector

• Arc

What formula is used to calculate the area of a circle?

• 2πr^2

• πr^2

• πr

• 2πr

If a sector's angle is 90 degrees, what fraction of the circle's area does it represent?

• 1/4

• 1/2

• 1/6

• 1/3

What is the formula for the circumference of a circle?

• r^2

• πd

• 2πr

• πr^2

If the radius of a circle is 6 cm, what is the length of an arc that represents a quarter of the circle?

• 37.68 cm

• 9.42 cm

• 18.84 cm

• 28.26 cm

How do you represent an angle of a sector as a fraction of a circle?

• Angle/270

• Angle/360

• Angle/90

• Angle/180

For an angle of 113 degrees, how is the fraction of the circle represented?

• 113/180

• 113/90

• 113/360

• 113/270

What is the area of a sector with a radius of 15 mm and an angle of 113 degrees?

• 222 mm^2

• 322 mm^2

• 422 mm^2

• 522 mm^2

What is the area of a sector with a 70-degree angle and a radius of 14 cm?

• 140 cm^2

• 130 cm^2

• 120 cm^2

• 150 cm^2

What is the length of an arc with a 70-degree angle and a radius of 14 cm?

• 16.1 cm

• 19.1 cm

• 17.1 cm

• 18.1 cm