Question 1: Calculate the area of a sector with a radius of 7 cm and a central angle of 60°.

Answer: 22π cm²

Question 2: Find the length of the arc of a sector with a radius of 10 meters and a central angle of 90°.

Answer: 15.7 meters

Question 3: A sector of a circle has a radius of 5 cm and an arc length of 8π cm. What is the measure of its central angle?

Answer: 288°

Question 4: Explain why the area of a sector with a central angle of 180° is exactly half the area of the circle.

Answer: Because a 180° sector covers half the circle, dividing the circle's area by 2 gives the sector's area.

Question 5: Plot a sector with a radius of 6 cm and a central angle of 120°. Shade the sector appropriately on the grid.

Answer: Student's drawing representing a 120° sector in a circle of radius 6 cm.

Question 6: A sector with a radius of 8 meters has an arc length of 20π meters. What is the measure of its central angle?

Answer: 150°

Question 7: Calculate the area of a sector with radius 12 cm and a central angle of 45°.

Answer: 4.2π cm²

Question 8: A circular garden has a sector that represents a 90° section. If the radius of the garden is 14 meters, find the length of the arc that bounds this sector.

Answer: 7π meters

Question 9: Identify and correct the mistake: A student claims that the area of a 60° sector with radius 10 cm is 100π cm².

Answer: Incorrect; the correct area is (10² × π × 60°/360°) = (100π × 1/6) = (50/3)π cm².

Question 10: Challenge: A sector has a radius of 9 cm and its area is 20π cm². Find the measure of its central angle.

Answer: 160°

Question 11: Determine the sector area in terms of π for a circle with radius 15 cm, if the central angle is 135°. Then, find the approximate numerical value.

Answer: 225π cm²; approximately 706.86 cm²