Arc Length Radian and Sector Area

A rope is being wound around a drum with a radius of 0.8725 ft. How much rope will be wound around the drum if the drum is rotated through an angle of 39.72°?

• 0.6049 ft

• 1.210 ft

• 17.33 ft

• 34.66 ft

What is the radian measure of the shaded angle?

What is a radian?

• a central angle created when the radius is wrapped around a circle.

• a central angle created when the radius is twice as big as the arc length

• a central angle created when the radius is half as big as the arc length

• a misspelling of radius

What is the radian measure of the shaded angle?

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

• 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°?

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