Question 1: Calculate the fraction of the circle that a sector with a central angle of 60° represents.

Answer: 1/6

Question 2: Find the area of a sector with radius 10 cm and a central angle of 90° using the formula: (θ/360) × πr².

Answer: 78.54 cm²

Question 3: A circle has a radius of 15 meters. What is the area of a sector with a central angle of 120°? Express your answer in square meters.

Answer: 1178.1 m²

Question 4: Construct a sector with a radius of 8 cm and a central angle of 45° on the grid. Show the sector clearly.

Answer: Student's drawing

Question 5: A pizza has a radius of 12 inches. If a slice has a central angle of 30°, what is the area of the pizza slice? Use π ≈ 3.14.

Answer: 37.68 in²

Question 6: Express the fraction of a circle represented by a sector with a 150° central angle.

Answer: 5/12

Question 7: Calculate the sector area for a circle with radius 20 cm and a central angle of 180°. Show your work.

Answer: 628.32 cm²

Question 8: A circular garden has a radius of 9 meters. A flower bed is created in a sector with a 90° angle. What is the area of the flower bed?

Answer: 113.1 m²

Question 9: A circular track has a radius of 50 meters. If a runner completes 1/4 of the track, what is the length of the path run?

Answer: 196.35 m

Question 10: Identify and correct the mistake in this calculation: A sector with a 60° angle and radius 10 cm is claimed to have an area of 10π cm². Is this correct? Why or why not?

Answer: Incorrect; actual area is (60/360)×π×10² = (1/6)×π×100 ≈ 52.36 cm², not 10π cm².

Question 11: Challenge: A sector with a central angle of 210° has an area of 150 cm². Find the radius of the circle.

Answer: ≈ 17.32 cm