Finding Arc Length in A3T 9.4

This video tutorial covers the concept of arc length in a circle, explaining the formula s = Rθ, where s is the arc length, R is the radius, and θ is the central angle in radians. It includes examples of calculating arc length, converting degrees to radians, finding the radius, and determining the central angle. The tutorial emphasizes the importance of using radian measure and provides step-by-step solutions to various problems.

What does the variable 's' represent in the arc length formula?

• The diameter of the circle

• The radius of the circle

• The central angle in radians

• The length of the arc

Why must the angle measure be in radians when using the arc length formula?

• Radians provide a more accurate measurement

• The formula only works with radians

• Degrees cannot be converted into a measurable length

• It's a preference, not a requirement

How do you convert degrees to radians?

• Multiply by π/180

• Divide by 180/π

• Divide by π/180

• Multiply by 180/π

What is the arc length when the radius is 3 inches and the central angle is π/6 radians?

• 3π/6 inches

• 1.5 inches

• 6/π inches

• π/2 inches

What is the approximate value of π/2 inches in decimal form?

• 1.57 inches

• 3.14 inches

• 0.785 inches

• 6.28 inches

If the radius of a circle is 4 inches and the central angle is 240 degrees, what is the arc length in radians before calculation?

• 2π/3 radians

• π/2 radians

• 3π/4 radians

• 4π/3 radians

What is the radius of a circle if a central angle of π/6 radians intercepts an arc with the length of 2.46 inches?

• Approximately 4.7 inches

• 2.46 inches

• π/6 inches

• 6/π inches

How do you find the measure of the central angle when given the arc length and radius?

• Divide the radius by the arc length

• Multiply the radius by π

• Divide the arc length by the radius

• Multiply the arc length by the radius

What is the central angle in radians if the arc length is 18 centimeters and the radius is 4.5 centimeters?

• 4 radians

• π radians

• 2π radians

• 1 radian

When solving for the radius given the arc length and central angle, what operation do you perform with the angle?

• None, the angle is not used

• Multiply by the angle

• Divide by the angle

• Multiply by the reciprocal of the angle