Arc Length and Sector Area- Degree AND Radian Measure

In a circle with a diameter of 24 cm, a central angle of  $\frac{4\pi}{3}$  radians intercepts an arc. The length of the arc, in terms of  $\pi$ , is

•  $16\pi$  

•  $4\pi$  

•  $3\pi$  

•  $32\pi$  

Tags

CCSS.HSF.TF.A.1

CCSS.HSG.C.B.5

In a circle with a diameter of 32, the area of a sector is  $\frac{512\pi}{3}$ . The measure of the angle of the sector, in radians, is

•  $\frac{\pi}{3}$  

•  $\frac{4\pi}{3}$  

•  $\frac{16\pi}{3}$  

•  $\frac{64\pi}{3}$  

In the diagram below, the circle shown has radius 10. Angle B intercepts an arc with a length of  $2\pi$ . What is the measure of angle B, in radians?

•  $10+2\pi$  

•  $20\pi$  

•  $\frac{\pi}{5}$  

•  $\frac{5}{\pi}$  

In circle O, the length of radius  is 9 centimeters and the area of sector AOB  is   $\frac{27\pi}{2}$  square centimeters. The measure of  in radians is          

•  $\frac{\pi}{3}$  

•  $3\pi$  

•  $\frac{1}{3\pi}$  

•  $\frac{3}{\pi}$  

Tags

CCSS.HSF.TF.A.1

CCSS.HSG.C.B.5

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

In the diagram below of circle O, the area of the shaded sector LOM is 2π  $cm^2$ . If the length of NL is 6 cm, what is m∠N in degrees? (HINT: Find angle LOM first then Recall the INSCRIBED ANGLE rule to find angle N)

• 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°?

• $\frac{8\pi}{3}$

• $\frac{16\pi}{3}$

• $\frac{32\pi}{3}$

• $\frac{64\pi}{3}$

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

• $\pi$ radians

• greater than $60\degree$

• $60\degree$