Find Arc Length and Radians Equations of Circles Review

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

• 10

• 20

• 40

• 80

What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures 60°?

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

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