Question 1: Given a circle with radius 7 cm, find the length of an arc that subtends a central angle of 60°.

Answer: 7.33

Question 2: Calculate the measure of the arc in degrees if it subtends a central angle of 150° in a circle.

Answer: 150

Question 3: A circle has a radius of 10 cm. An arc subtends a central angle of 90°. Find the length of this arc.

Answer: 15.71

Question 4: Construct an arc in your diagram with a radius of 8 cm that subtends a 45° angle at the center. Label the arc and central angle.

Answer: Student-constructed diagram

Question 5: In a circle with radius 12 cm, an arc measures 36°. Calculate the length of the arc.

Answer: 7.54

Question 6: A central angle of 120° subtends an arc in a circle. If the radius of the circle is 9 cm, what is the length of the arc?

Answer: 18.85

Question 7: A circular track has a radius of 50 meters. A runner completes an arc of 60° at the track. How long is this arc?

Answer: 52.36 meters

Question 8: The circumference of a circle is 31.4 cm. Find the measure in degrees of an arc that is 10 cm long.

Answer: 114.59

Question 9: A sector of a circle has a radius of 9 cm and an arc length of 15.7 cm. Determine the measure of the central angle in degrees.

Answer: 100.8

Question 10: Identify and explain the common mistake students make when calculating the length of an arc given the central angle. How would you correct it?

Answer: Often students confuse the proportion of the angle with the full circle; they may multiply the radius by the angle in radians directly. To correct this, remind students to convert the angle to radians before calculation or use the arc length formula directly involving degrees: (θ/360) * 2πr.

Question 11: A circle's radius is 15 cm. An arc subtends a 210° angle at the center. Calculate the length of this arc.

Answer: 27.63