Arc Length, Sector Area, Linear and Angular Speed

Calculate the length of an arc with radius 15 cm and central angle of 30°.

• 450 cm
• 5π/2 cm or ≈ 7.9 cm
• 225 cm
• 5π/4 cm or ≈ 3.9 cm

Calculate the area of a sector with central angle of 140° and radius of 8 cm.

• 224/9 cm² or ≈ 24.9 cm²
• 896 π/9 cm² or ≈ 312.8 cm²
• 4480 cm²
• 224 π/ 9 cm² or ≈ 78.2 cm²

Determine the central angle if the arc length is 10 cm and the radius is 5 cm.

• 2°
• not possible ... "s" is too small
• ≈ 114.6°
• 360°

What is the radius of the circle with area of a sector equal to 7π cm² and central angle of 70°?

• 6 cm
• 1π/5 cm or .6 cm
• .8 cm
• 36 cm

A ceiling fan with 16 inch blades rotates at 45 rpm.  Find the angular velocity of the fan in rad/min.  Round to the nearest tenth.

• 90 rad/min
• 282.7 rad/min
• 45 rad/min
• 141.4

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.

• 5654.9 in/min
• 1800 in/min
• 2827.4 in/min
• 900 in/min

How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile?  (Hint:  determine the circumference first ... rev/circumference ... then convert to rev/mile)  Round answer to the nearest tenth.

• 6635.0 rev/mile
• 672.3 rev/mile
• 884.7 rev/mile

The wheels of a car have radius 11 in. and are rotating at 600 rpm.  Determine the speed of the car in miles/hour to the nearest tenth.  (Determine ω (angular velocity) first and then use v=ω⋅r and convert to miles/hour)

• 6.3 miles/hour
• 12.5 miles/hour
• 39.3 miles/hour
• 78.5 miles/hour

Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.

• 360π rad/min
• 12π rad/min
• 360 rad/min
• 720π rad/min