Question 1: Calculate the measure of the central angle of a sector that makes up one quarter of a circle.

Answer: 90

Question 2: Find the area of a sector with a radius of 10 cm and a central angle of 60°.

Answer: approx. 26.18 cm^2

Question 3: A circle has a radius of 15 meters. What is the length of the arc corresponding to a 120° sector?

Answer: approx. 62.83 meters

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

Answer: Student's drawn sector with annotations

Question 5: Calculate the area of a sector with a radius of 12 cm and a central angle of 90°.

Answer: approx. 150.80 cm^2

Question 6: A circular garden has a radius of 20 meters. If a 60° sector is sectioned off, what is the area of that sector?

Answer: approx. 69.81 m^2

Question 7: Express the area of a sector with radius 9 cm and central angle 30° as a fraction of the total circle's area.

Answer: 1/12

Question 8: Calculate the length of a 45° arc of a circle with radius 14 cm.

Answer: approx. 11.0 cm

Question 9: Determine the central angle of a sector that has an area of 20 cm^2 in a circle with radius 10 cm.

Answer: approx. 36.87°

Question 10: A sector of a circle has an area of 15π cm^2 and a radius of 5 cm. Find the measure of its central angle.

Answer: 180°

Question 11: Identify and correct the mistake: A student calculates the area of a sector with radius 10 cm and central angle 90° as 100 cm^2.

Answer: Incorrect; correct area is (π×10^2)×(90/360)=25π ≈78.54 cm^2

Question 12: Challenge: A segment of a circle is cut off by a chord, forming a sector with a radius of 10 cm and a central angle of 150°. Calculate the area of the segment (the area between the chord and the arc).

Answer: approx. 36.62 cm^2