Question 1: Calculate the measure of the arc subtended by a central angle of 60° in a circle with radius 10 cm.

Answer: 10π cm or approximately 31.42 cm

Question 2: In a circle of radius 15 cm, an arc measures 90°. Find the length of this arc.

Answer: 7.5π cm or approximately 23.56 cm

Question 3: A sector of a circle has a radius of 8 cm and an arc length of 12.56 cm. What is the measure of the central angle in degrees?

Answer: 180°

Question 4: Construct a diagram showing a circle with a radius of 12 cm and mark an arc that measures 60°. Use the grid to assist with drawing.

Answer: Student draws circle with radius 12 cm, marks an arc with 60° central angle

Question 5: A runner completes a 2 km circular track in 10 minutes. If the central angle of the arc they run along is 45°, what is the length of the arc covered in that time?

Answer: 1 km

Question 6: Determine the measure of an inscribed angle that subtends an arc of 100°.

Answer: 50°

Question 7: Calculate the length of an arc in a circle with radius 20 cm that subtends a central angle of 150°.

Answer: 50π cm or approximately 157.08 cm

Question 8: A sector with a radius of 9 cm has an arc length of 15.7 cm. What is the measure of the central angle in degrees?

Answer: 100°

Question 9: A circular garden has a radius of 5 m. An irrigation system covers an arc of 60°. Find the length of the watered area.

Answer: about 5.24 meters

Question 10: Identify and correct the mistake: A student states that the length of an arc is equal to the measure of the central angle in degrees.

Answer: The arc length depends on the radius as well; it's not equal to the angle in degrees.

Question 11: Challenge: A semicircular arch has a radius of 3 meters. Calculate the length of the arch (the curved part).

Answer: 3π meters or approximately 9.42 meters