Exploring Arc Length and Sector Area

The video tutorial covers the concept of arc length and the area of sectors in circles. It explains how to calculate arc length using radians and convert degrees to radians. The tutorial also includes solving word problems related to arc length and finding the area of sectors. Additionally, there is a casual discussion about a concert experience.

What is the formula for calculating the arc length?

• S = R - Theta

• S = R * Theta

• S = R / Theta

• S = R + Theta

In a circle with radius 3 and central angle 5pi/6 radians, what is the arc length?

• 15pi/6 feet

• 5pi/2 feet

• 5pi/6 feet

• 3pi/2 feet

Why must Theta be in radians for the arc length formula to work?

• Radians are easier to calculate with.

• The formula only works with radians.

• Degrees are not precise enough.

• Radians and degrees are interchangeable.

How do you convert degrees to radians?

• Multiply by pi/180

• Divide by 180/pi

• Multiply by 180/pi

• Divide by pi/180

When converting an angle from degrees to radians, what is the first step?

• Subtract 180

• Multiply by pi/180

• Add pi

• Divide by pi

For an angle measure given in degrees, what is the necessary conversion for calculating arc length?

• Convert to radians using 180/pi

• Multiply by 2pi

• Convert to radians using pi/180

• No conversion is necessary

If the radius of a circle is 8 meters and the central angle is 78pi/5 radians, what is the arc length?

• 624pi/5 meters

• 156pi/5 meters

• 78pi/5 meters

• 8pi meters

How is the area of a sector calculated?

• 2 * pi * r * Theta

• pi * r^2 * Theta

• r * Theta

• 1/2 * r^2 * Theta

What is the arc length if the central angle is 5.4 degrees and the radius is 396 miles?

• 37.8 miles

• 21 miles

• 5.4 miles

• None of the above

What is the radius of a circle if the area of a sector with a central angle of 240° is 134 ft²?

• 8 feet

• 6 feet

• 10 feet

• 12 feet