Arc Length Practice

What is the formula to find the arc length of a circle?

• Arc Length = r * θ, where r is the radius and θ is the central angle in radians.

• Arc Length = 2 * π * r

• Arc Length = r^2 * θ

• Arc Length = θ / r

How do you find the radius if you know the arc length and the central angle in radians?

• Radius = Arc Length / Central Angle.

• Radius = Central Angle / Arc Length.

• Radius = Arc Length * Central Angle.

• Radius = Arc Length + Central Angle.

How do you convert degrees to radians?

• Multiply by π/180

• Add 180 to the degree value

• Divide by 180

• Multiply by 180/π

What is the significance of the unit circle in understanding arc length?

• It helps visualize the relationship between angles in radians and arc lengths, as the radius is 1.

• It provides a method to calculate the area of a circle.

• It shows the relationship between degrees and radians only.

• It is used to determine the circumference of any circle.

What is a central angle?

• An angle whose vertex is at the center of the circle and whose sides intersect the circle.

• An angle formed by two radii of a circle.

• An angle that is greater than 180 degrees.

• An angle that is less than 90 degrees.

What is the radian measure of a full circle?

• π radians

• 2π radians

• 3π radians

• 4π radians

How do you find the length of an arc when given the angle in degrees?

• Use the formula Arc Length = r * θ directly without conversion.

• Convert the angle to radians first, then use the formula Arc Length = r * θ.

• Multiply the angle in degrees by 2π to find the arc length.

• Use the formula Arc Length = θ * r^2.

If an arc length is 15 cm and the radius is 5 cm, what is the central angle in radians?

• 1.5 radians

• 2 radians

• 3 radians

• 4 radians

If the radius of a circle is doubled, how does the arc length change for the same central angle?

• The arc length remains the same.

• The arc length triples.

• The arc length also doubles.

• The arc length decreases by half.

What is the arc length of a circle with a radius of 8 inches and a central angle of 45 degrees?

• 2 inches

• 4 inches

• 2π inches

• 8 inches