Question 1: A circle has a radius of 10 cm. Calculate the area of a sector with a central angle of 60°.

Answer: 87.96

Question 2: Find the measure of the central angle of a sector if the sector's area is 50 cm² and the circle's radius is 8 cm.

Answer: 96.25

Question 3: Construct a sector with a radius of 7 cm and a central angle of 45°. Shade the sector on the grid.

Answer: Constructed sector with radius 7cm, angle 45°

Question 4: Calculate the length of the arc of a sector with a radius of 12 cm and a central angle of 90°. (Use π ≈ 3.14)

Answer: 37.68

Question 5: A circular garden has a radius of 15 meters. If a sector of 120° is sectioned off for planting, what is the area of this sector?

Answer: 117.81

Question 6: The central angle of a sector is 150°, and the radius of the circle is 9 cm. Find the area of the sector.

Answer: 53.41

Question 7: A sector of a circle has an area of 20 cm² and a radius of 5 cm. What is the measure of its central angle?

Answer: 45

Question 8: Identify the common mistake: A student calculates the sector area using the formula  imes ext{radius} imes ext{arc length} without dividing by 2. Explain and correct the error.

Answer: The student used the formula for the area of a triangle, not a sector. Correct formula: (θ/360) × π × r^2.

Question 9: A sector with a central angle of 30° has an arc length of 5 cm. Find the radius of the circle.

Answer: 9.55

Question 10: A pie chart shows 25% of data in a sector. If the circle's radius is 6 cm, what is the area of this sector?

Answer: 7.07

Question 11: Calculate the sector area for a circle with radius 14 cm and a central angle of 90°. Use π ≈ 3.14.

Answer: 69.96

Question 12: Challenge: Derive the formula for the area of a sector starting from the circle's total area. Explain each step briefly.

Answer: Total area of circle = πr^2. Sector area = (θ/360) × πr^2, derived by proportion of the circle's area based on the central angle.