Question 1: Calculate the angle of a sector that subtends an arc of 60 degrees in a circle.

Answer: 60

Question 2: A sector of a circle has a radius of 10 cm and a central angle of 90 degrees. Find the area of the sector.

Answer: 78.54

Question 3: What is the fraction of the circle that a sector with a 45-degree angle represents?

Answer: 1/8

Question 4: Construct a sector with a radius of 8 cm and a central angle of 120 degrees on the grid. Show all steps.

Answer:

Question 5: A pizza is cut into 8 equal sectors. If one sector has an arc length of 15 cm and the radius is 10 cm, verify the calculation of the sector's angle.

Answer: 45

Question 6: A circular garden has a sector with a radius of 15 meters and a central angle of 30 degrees. Find the area of the sector.

Answer: 11.78

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

Answer: 91.02

Question 8: Calculate the arc length of a sector with a radius of 12 cm and a central angle of 150 degrees.

Answer: 31.42

Question 9: A sector’s central angle is 60 degrees, and its area is 15.7 cm². Find the radius of the circle.

Answer: 6.4

Question 10: Identify and correct the mistake in this calculation: The area of a sector with radius 7 cm and central angle 90 degrees is calculated as (π * 7² * 90)/360 = 21.99 cm².

Answer: The correct area is (π * 7² * 90)/360 ≈ 38.48 cm²

Question 11: A circular track has a sector with a radius of 50 meters and a central angle of 120 degrees. Calculate the length of the arc and the area of the sector.

Answer: Arc length: 104.72 m; Sector area: 523.6 m²