Arc Length and Sector Area

Arc Length & Area of a Sector

Objective: Use proportional reasoning to find arc length and area of a sector

Multiple Choice

Find the circumference of the circle

• 50.24 yd

• 25.12 yd

• 11.14 yd

Arc Length

Ex 1: Find the length of the minor arc

Area =  πr²

Multiple Choice

Find the area of a circle with a diameter of 28 meters.

• 43.96 m²

• 615.44 m²

• 87.92 m²

• 2461.76 m²

Area of a Sector

Ex 1:

Multiple Choice

Find the arc length of arc AB.

• 12.57 units
• 75.40 units
• 24 units
• 125.66 units

Multiple Choice

Find the arc length of arc AB.

• 1.5 units
• 18.85 units
• 4.71 units
• 200 units

Multiple Choice

Find the estimated area of the shaded area.

• 10.732 units squared
• 100.53 units squared
• 9.75 units squared
• 3,015.93 units squared

Multiple Choice

Find the area of the shaded space.

• 113.10 units squared
• 150.80 units squared
• 157.82 units squared
• 10.92 units squared

Multiple Choice

Stephanie was jogging around circular track. One part of the track was darker than the rest. She found the angle to be 270 degrees. She found the diameter was thirty feet. What is the arc length around the darker part of the track she jogged on? (rounded to the nearest whole number)

• 71 feet
• 141 feet
• 84 feet
• 63 feet

Multiple Choice

Stephanie is cutting a pie. Stephanie's mother wants one fourth of the pie. The diameter is 20 cm. What is the sector area of the pie her mother does not want?

• 235.62 cm squared
• three fourths of the pie
• 78.54 cm squared
• 83.99 cm squared

Multiple Choice

Rob is trying to open a can. He wants to find the arc length the can opener needs to travel to open the can half way. The radius of the can is 1.5 inches.

• 10 inches
• 2 feet
• 4.71 inches
• 3.53 inches

Multiple Choice

Find the arc length.

• 5.50 cm
• 11.00 cm
• 0.39 cm
• 141.37 cm

Multiple Choice

Find the arc length of the bolded arc.

• A
• B
• C
• D

Multiple Choice

Find the area of the sector.

• A
• B
• C
• D

Multiple Choice

Find the arc length of the bolded arc.

• A
• B
• C
• D

Multiple Choice

Find the area of the shaded sector.

• 9.23 in²
• 10.51 in²
• 31.42 in²
• 38.27 in²

Multiple Choice

What is the area of the shaded region?

• 50.27 units²
• 3015.93 units²
• 8.38 units²
• 4.19 units²

Multiple Choice

What is the area of the shaded region? Round to the nearest hundredth.

• 1.26 units²
• 452.39 units²
• 113.10 units²
• 40,715.04 units²

Multiple Choice

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?

• 161.97 mm²
• What's Pacman?
• 39.1 mm²
• 9.77 mm²

Multiple Choice

Find the area of the shaded sector

• 173.42 cm²
• 212.06 cm²
• 237.50 cm²
• not enough information

Multiple Choice

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40
• 35
• 55
• 69

Multiple Choice

A cathedral window is shown. If the window is to contain three stained glass sections of equal size, what is the area of EACH stained glass section?  Express answer to the nearest square foot.

• 1 ft²
• 13 ft²
• 3 ft²
• 26 ft²

Multiple Choice

Find the area of the shaded sector.

• 37.70 cm²
• 6.28 cm²
• 28.27 cm²
• 9.42 cm²

Multiple Choice

Find the arc length.

• 37.70 cm
• 6.28 cm
• 28.27 cm
• 9.42 cm

Multiple Choice

Find the area of the shaded sector.

• 11.31 cm²
• 3.77 cm²
• 7.54 cm²
• 23.56 cm²

Multiple Choice

Find the arc length.

• 11.31 cm
• 3.77 cm
• 7.54 cm
• 23.56 cm

Multiple Choice

Find the length of the minor arc.

• 5.24 units
• 1.88 units
• 2.62 units
• 3.77 units

Multiple Choice

What is the area of the indicated region?

• A
• B
• C
• D