Arc Length to Area of a Sector

Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to thenearest tenth of a square unit.

• 0.3 square units

• 15.7 square units

• 19.7 square units

• 50.3 square units

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47

• 74

• 94

• 123

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

• 7/4π

• 7/2π

• 1/8π

• 45π

The distance along an arc measured in linear units.

• area of a sector

• arc length

• arc of a circle

• sector of a circle

Match the answers to the following problems.

• Problem 3

• Problem 2

• Problem 4

• Problem 1

Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch.

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Find the area of a sector with an arc length of 30 cm and a radius of 8 cm.

• 240 cm²

• 80 cm²

• 120 cm²

• 180 cm²

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

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

• 7/4π

• 7/2π

• 1/8π

• 45π

Find the length of the bold arc.Leave pi in your answer.

• 5688π ft

• 15.8π ft

• 150.4π ft

• 54,150 ft