Arc Length & Sector Area: Geometry Challenge for 10th Graders

A circular park has a radius of 10 meters. What is the arc length of a path that subtends a central angle of 60 degrees at the center of the park?

• 15.71 meters

• 5.24 meters

• 20.00 meters

• 10.47 meters

A pizza has a radius of 12 inches. If a slice of pizza represents a sector with a central angle of 45 degrees, what is the area of that slice?

• 18π square inches

• 36π square inches

• 12π square inches

• 24π square inches

A clock has a minute hand that is 15 cm long. How long is the arc traced by the minute hand in 10 minutes?

• 15.71 cm

• 20 cm

• 10.5 cm

• 12.6 cm

A circular swimming pool has a diameter of 20 feet. If a sector of the pool is shaded, covering a central angle of 90 degrees, what is the area of the shaded sector?

• 15π square feet

• 25π square feet

• 10π square feet

• 40π square feet

A bicycle wheel has a radius of 0.35 meters. If the wheel makes one complete revolution, what is the distance traveled along the circumference?

• 2.5 meters

• 1.5 meters

• 3.14 meters

• Approximately 2.199 meters

A sector of a circle has a radius of 5 cm and a central angle of 120 degrees. Calculate the area of the sector.

• 25.13 cm²

• 20.94 cm²

• 30.42 cm²

• 15.71 cm²

A garden is designed in the shape of a sector with a radius of 8 meters and a central angle of 30 degrees. What is the area of the garden?

• 20 square meters

• 10.5 square meters

• 25 square meters

• 16.76 square meters

A circular track has a radius of 50 meters. If a runner runs along an arc that subtends a central angle of 90 degrees, how far does the runner travel?

• 25π meters

• 75π meters

• 100 meters

• 50 meters

A cake is shaped like a circle with a radius of 10 inches. If a piece of the cake is cut out with a central angle of 72 degrees, what is the area of the remaining cake?

• 80π square inches

• 36π square inches

• 100π square inches

• 50π square inches

A circular fountain has a radius of 4 meters. If a section of the fountain is covered with tiles that form a sector with a central angle of 150 degrees, what is the area of the tiled section?

• 15.70 square meters

• 30.00 square meters

• 20.94 square meters

• 25.12 square meters