Applications of Radian Measure

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

If the length of the 45° region of this circle is 10 inches, what is the radius of the circle?

• 6in

• 3in

• 6.8in

• 2.5in

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the angular speed in radians per hour?

• 90π rad / 1 hr

• 2700π rad / 1 hr

• 5400π rad / 1 hr

• 97200π rad / 1 hr

A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle?

• 7.78 inches

• 8.21 inches

• 157.5 inches

• 7 inches

• A

• B

• C

• D

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 central angle?

• 1.5

• 3

• 4

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

• 1.5

• 3

• 4

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

• 1

• 2

• 0

Jacob jogs on a circular track that has a radius of 142 feet. He runs from point T to U, which is 320 feet. To the nearest tenth of a radian, find the measure of arc TU.

• 2.3 radians

• 0.4 radians

• 2.2 radians

• 4.5 radians