Arc Length Using Radians

A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?

• 63

• 31

• 20

• 10

Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length, in yards, of the border (arc length)?

• .5

• 2

• 5

• 7.5

A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius of the garden?

• 8 ft

• 50 ft

• 100 ft

• 125 ft

A pizza has a radius of 12 inches and is cut into 8 equal slices. What is the arc length of one slice?

• 3π inches

• 6π inches

• 4.5π inches

• 1.5π inches

The diameter of a circle is 8 centimeters. A central angle of the circle intercepts an arc of 12 centimeters. What is the radian measure of the angle?

Mathematical Equivalence

ON

What is the length of arc BB'?

In circle O, the length of radius OB is 5 centimeters and the length of AB is 5 centimeters. The measure of ∠AOB is (HINT: Try solving for the angle using both the radian and degree formulas and see which answer makes sense with the multiple choice options) 

• 1 radian

Circle A has a radius of 8 cm. The measure of central angle CAB is 2.5 radians. What is the length of the intercepted arc CB?

• 20 cm

• 16.5 cm

• 8.5 cm

• 3.2 cm