The distance along a portion of a circle's circumference, determined by the central angle and the radius.
Imagine walking along a circular track but only covering a portion of the full loop. The arc length is how far you actually walked. If you walk a quarter of the circle (90°), you cover a quarter of the circumference. The fraction of the full circle you cover determines the fraction of the circumference you walk.
Showing a random 20 of 50 problems.
Example 1
medium
An arc has length 10 m on a circle of radius 4 m. Find the central angle in degrees (to the nearest degree).
Example 2
easy
A 30° arc in a circle of radius 6. Find its arc length in terms of π.
Example 3
medium
Convert: a 30° arc has what arc length in a circle of radius 18 (in terms of π)?Find the arc length of a 30° arc in a circle of radius 18
Example 4
easy
A full circle has radius 7. What is the arc length for 360°? (in terms of π)Arc length for a full 360° arc in a circle of radius 7
Example 5
medium
Find the arc length on a circle of radius 15 subtended by a central angle of 52π radians.
Example 6
easy
Two circles, radii 3 and 6, each have a 90° arc. How do the arc lengths compare?
Example 7
easy
What is the formula for arc length given a central angle θ (in degrees) and radius r?
Example 8
hard
A racetrack has two straight 100 m sections connected by two semicircular ends of radius 30 m. What is the total length of one lap?
Example 9
easy
A circle has a radius of 10 cm. What is the arc length for a central angle of 90°?Arc length for a 90° central angle in a circle of radius 10 cm
Example 10
challenge
Earth's radius is about 6371 km. Two cities lie on the same meridian, 5° of latitude apart. Find the distance between them along the surface.
Example 11
medium
An arc of 45° has length 2π. Find the radius.Given a 45° arc of length 2π, find the radius
Example 12
easy
Find the arc length for a 90° arc in a circle of radius 8 (in terms of π).Find the arc length of a 90° arc in a circle of radius 8
Example 13
easy
How does arc length differ from arc (degree) measure?
Example 14
easy
A circle has radius 6 cm. Find the arc length intercepted by a central angle of 60°.Arc length intercepted by a 60° central angle in a circle of radius 6 cm
Example 15
hard
Two pulleys with radii 4 and 9 rotate so the linear speed of their belts is the same. If the larger pulley rotates at ω2=4 rad/s, find ω1 (the smaller pulley's angular speed).
Example 16
challenge
A circular running track has inner radius 36.5 m. An athlete runs 400 m along the inner edge. Through how many radians has the athlete moved? Round to two decimals.
Example 17
easy
A circle has circumference 24π. Find the arc length of a 90° arc.
Example 18
challenge
Earth's radius is approximately 6371 km. A 1° change in latitude corresponds to how many kilometers of arc length along a meridian? Round to the nearest km.
Example 19
challenge
A goat is tied to the corner of a 10×10 m square shed with a 15 m rope. Find the total area... first find the arc length the rope sweeps in the open region (a 270° arc of radius 15).Goat tied at a corner of a 10×10 shed with a 15 m rope sweeps a 270° arc
Example 20
easy
A 120° arc in a circle of radius 9. Find its arc length in terms of π.Find the arc length of a 120° arc in a circle of radius 9