Radian Measure Worksheets Grade 11

1. An astronomer is tracking the International Space Station as it orbits Earth. During a 30-minute observation window, the ISS sweeps out a central angle of 1.8 radians relative to Earth's center. If the ISS orbits at an altitude where its orbital radius (distance from Earth's center) is 6,780 km, what distance along its orbital path does the ISS travel during this observation period?
2. A circle has radius 8 cm. An arc subtends an angle of 2π/3 radians at the center. Find the arc length.
3. A robotic arm in a manufacturing plant rotates through a central angle of 3π/4 radians to move components between two workstations. If the tip of the arm travels an arc length of 4.71 meters during this rotation, what is the length of the robotic arm from its pivot point to the tip?

…and 4 more problems

1. An engineer is designing a curved highway exit ramp that follows the arc of a circle with radius 120 meters. The ramp needs to be exactly 94.2 meters long. What central angle (in radians) should the engineer use for this curved section of the highway?
2. 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?
3. A circle has radius 8 cm and a central angle of 3π/4 radians. Find the arc length = ?

…and 1 more problems

1. A sector of a circle has area 24π cm² and central angle 2π/3 radians. Find the radius of the circle: r = ?
2. A sector of a circle has radius 12 cm and arc length 10π cm. Find the central angle in radians: θ = ?
3. A central angle of π/3 radians intercepts an arc of length 5π cm. Find the radius of the circle.

…and 2 more problems