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

Answer: 1/6

Question 2: Find the area of a sector with a radius of 10 cm and a central angle of 90°.

Answer: 78.54

Question 3: What fraction of a full circle is a sector with an angle of 150°?

Answer: 5/12

Question 4: Calculate the area of a sector with radius 7 cm and central angle 120°. (Use π ≈ 3.14)

Answer: 25.96

Question 5: A circle has a radius of 15 cm. What is the area of a sector with a central angle of 45°?

Answer: 35.34

Question 6: A sector with an angle of 180° is cut out from a circle of radius 8 cm. Calculate the area of this sector.

Answer: 100.53

Question 7: Construct a sector with a radius of 12 cm and a central angle of 90° on your grid. What is the area of the sector? (Use π ≈ 3.14)

Answer: 135.72

Question 8: If a sector has an area of 50 cm² and a radius of 10 cm, what is its central angle?

Answer: 60°

Question 9: A pie chart shows that 1/4 of the chart is a sector with a central angle of 90°. What is the total angle of the circle in degrees?

Answer: 360

Question 10: A sector with a 135° angle is shaded on a circle of radius 9 cm. Calculate the shaded area.

Answer: 37.87

Question 11: Identify and correct the mistake: A student calculates the sector area of a 60° sector with radius 10 cm as 314 cm². Explain and correct the calculation.

Answer: The student used the full circle area (πr²=314) instead of the sector area. Correct calculation: (60/360)×π×10²= (1/6)×314=52.36 cm².