Arc Length and Sector Area

What is the ϴ called?

• Central angle

• Peripheral angle

• Acute angle

• Obtuse angle

Find the measure of arc AB if the total circumference is 340 degrees and the arc measures 68 degrees.

• 45 degrees

• 60 degrees

• 68 degrees

• 75 degrees

What is the difference between a sector and a segment in a circle?

• A sector is the area enclosed by two radii and the arc, while a segment is the area between a chord and the arc.

• A sector is a part of the circle defined by a single radius, while a segment is the entire circle.

• A sector is the area of the circle divided by the diameter, while a segment is the area above the chord.

• A sector is the area enclosed by the circumference and a radius, while a segment is the area below the chord.

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the area of the sector?

• 10.47 cm²

• 15.71 cm²

• 17.45 cm²

• 20.94 cm²

What is the formula for the area of a sector?

• Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

• Area = π * r²

• Area = 2 * π * r

• Area = (θ/180) * π * r²

If the radius of a circle is 5 cm and the central angle is 90 degrees, what is the length of the arc?

• 5.00 cm

• 7.85 cm

• 10.00 cm

• 15.70 cm

How do you convert radians to degrees?

• Degrees = Radians * (180/π)

• Degrees = Radians * (360/π)

• Degrees = Radians * (180/2π)

• Degrees = Radians * (90/π)

If the total circumference of a circle is 100 cm, what is the length of an arc that subtends a central angle of 90 degrees?

• 15 cm

• 20 cm

• 25 cm

• 30 cm

What is the formula for arc length?

• Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

• Arc Length = θ * r, where θ is in radians.

• Arc Length = 2πr, where r is the radius.

• Arc Length = (θ/180) * πr, where θ is the central angle in degrees.

What is the relationship between the central angle and the arc length?

• The arc length is inversely proportional to the central angle; as the angle increases, the arc length decreases.

• The arc length is directly proportional to the central angle; as the angle increases, the arc length increases.

• The arc length is independent of the central angle; changes in the angle do not affect the arc length.

• The arc length is equal to the central angle; they are always the same.