Understanding Arc Length and Sector Area

The video tutorial explains how to calculate the length of an arc in a circle using the formula L = r * θ, where θ must be in radians. It provides examples with angles of 60 and 120 degrees, converting these angles to radians before calculating the arc length. The tutorial also introduces the concept of calculating the area of a sector, setting the stage for further exploration of this topic.

What is the formula for calculating the length of an arc?

• Radius times angle in radians

• Diameter times angle in degrees

• Diameter times angle in radians

• Radius times angle in degrees

How do you convert 60 degrees to radians?

• Multiply by π/180

• Multiply by 180/π

• Divide by π/180

• Divide by 180/π

What is the length of the arc when the radius is 3 and the angle is 60 degrees?

• 2π

• π

• 3π

• π/2

What is the radian measure of 120 degrees?

• π/3

• π/2

• 3π/2

• 2π/3

If the radius is 2 and the angle is 120 degrees, what is the length of the arc?

• 4π/3

• 2π/3

• π/3

• 3π/2

What is the first step in finding the length of an arc when given the angle in degrees?

• Add the angle to the radius

• Multiply the angle by the radius

• Convert the angle to radians

• Divide the angle by the radius

What is the relationship between degrees and radians?

• 180 degrees equals π radians

• 360 degrees equals π radians

• 90 degrees equals π radians

• 180 degrees equals 2π radians

What is the formula for converting degrees to radians?

• Degrees ÷ π/180

• Degrees × 180/π

• Degrees × π/180

• Degrees ÷ 180/π

What is the next topic introduced after arc length calculations?

• Surface area of a cylinder

• Volume of a sphere

• Area of a sector

• Circumference of a circle

What is the approximate decimal value of π?

• 5.14

• 4.14

• 3.14

• 2.14