Radian Measure Worksheets Grade 11

1. Liam is designing a circular running track for his school's new athletic facility. The track has a radius of 45 meters. He needs to install special rubberized surfacing along an arc that spans an angle of 2.1 radians. What length of surfacing material (in meters) should Liam order for this arc section?
2. 2π/3 radians × (180/π) = ?
3. Charlotte is designing a circular fountain for a park. The fountain has a radius of 9 meters, and she wants to place a decorative tile border along an arc that corresponds to a central angle of 5π/7 radians. What is the exact length of the arc (in meters) that will have the tile border? (Express your answer in terms of π.)

…and 2 more problems

1. Liam is designing a circular garden with a central fountain. The garden has a radius of 8 meters, and he wants to install a decorative stone path along an arc that subtends an angle of 2.1 radians at the center. What is the length of the stone path Liam needs to install?
2. Zoe is designing a circular fountain for a park. The fountain will have a radius of 12 meters. A decorative light strip will be installed along an arc that subtends a central angle of 1 radians. How long, in meters, will the light strip be?
3. A circular race track has a radius of 150 meters. A car travels along the track covering a central angle of 2.4 radians. What is the distance traveled by the car along the track?

…and 1 more problems

1. An astronomer is tracking a comet's path through the solar system. The comet follows a nearly circular orbit with a radius of 3.8 × 10^8 km. During a particular observation window, the comet sweeps out a central angle of 1.9 radians. What distance does the comet travel along its orbital path during this observation?
2. Mason is examining a circular gear in a machine. The gear has a radius of 9 centimeters. A small mark on the edge of the gear rotates through an angle of 7π/12 radians. What is the exact length of the arc traced by the mark along the circumference of the gear? (Express your answer in terms of π.)
3. Amelia is a cartographer creating a map of a circular city park. The park has a radius of 20 kilometers. Two landmarks are located along the park's boundary, and the angle between the lines from the center to these landmarks is 5 radians. What is the distance along the curved path between the two landmarks?