Arc Length

Vocab

100

the length of its “portion” of the circumference

length of an arc

200

Length of a circle

circumference

300

a “portion” of the circumference of the circle

arc of a circle

400

is defined as the ratio of the length of the arc the angle subtends, s, divided by the radius of the circle, r

Radian Measure

500

is equal to the measure of the central angle that intercepts the arc

the degree measure of an arc

Find the Length

100

θ = 2 and r = 4.3 inches

8.6in

200

r = 4in and θ= 60°

20.94in

300

8cm, 60 degrees

8.38cm

400

9yd, 75 degrees

5.89yd

500

12 feet, 173 degrees

18.12ft

Find the Area

100

Radius = 7.6in, Angle = 220°

110.81in²

200

Radius = 5.5cm, Angle = 77°

2.06cm²

300

Radius = 4.2yd, Angle = 346°

53.26yd²

400

Radius = 5m, Angle = 146°

31.85m²

500

Radius = 6.2ft, Angle = 115°

38.58ft²

Word Problems

100

An adjustable-angle pop-up lawn sprinkler has been installed in an awkward corner of the neighbor's yard. This sprinkler, assuming full water pressure, can spray everything within four meters. Given that the angle has been set to 70°, how much lawn will this sprinkler head water? (Round to two decimal places.)

9.77 m²

200

On a certain vehicle, one windshield wiper is 60 cm long, and is afixed to a swing arm which is 72 cm long from pivot point to wiper-blade tip. If the swing arm turns through 105°, what area of the windshield, to the nearest square centimeter, is swept by the wiper blade?

4750-132

4618 cm²

300

A 40 -inch pendulum swings through an angle of ο 18 . Find the length of the arc in inches through which the tip of the pendulum swings.

12.57in

400

This is the first year Janis is playing softball. She has been practicing her batting. On her last swing the bat made an arc with a radius of 48 inches and swept through 255° of rotation. Assuming the arc is circular, what is the distance the tip of the bat travels to the nearest inch? How many feet is this rounded to the nearest foot?

200ft

500

At Mickey’s Mechanic Shop a pulley system is used to lift engines from cars. The pulley system consists of a cable that goes around a pulley with a radius 1 ft. To the nearest degree, how many degrees of rotation are required for an engine to be lifted 10 feet?

1.59

Try Your Luck

100

arc length of 

12in, 210 degrees

43.98

200

arc area of 

14yd, 270 degrees 

461.58yd²

300

Arc length=

(Central angle/360)*circumference

400

area of a sector

(θ/360)*πr²

500

Who wins??

Us.

JK, the ____ team