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

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute.  What is the angular speed in radians per hour?

• 90π rad / 1 hr
• 2700π rad / 1 hr
• 5400π rad / 1 hr
• 97200π rad / 1 hr

A car tire has a diameter of 14 inches and is spinning at a of 10 revolutions per second. What is the linear speed in miles per hour?

• 7.95π mi / 1 hr
• 15.90 mi / 1 hr
• 3.28 rad / 1 hr
• 2.84 rad / 1 hr

A car tire has a diameter of 14 inches and is spinning at a rate of 10 revolutions per second. What is the angular speed in radians per hour?

• 120π rad / 1 hr
• 1,008,000π rad / 1 hr
• 504,000π rad / 1 hr
• 7200π rad / 1 hr

Find the angle generated by point P in time when r = 20 cm, w=pi/12 per sec and t = 6 sec.

• Pi/2

• pi

• pi/12

• 6

Find the linear speed of P when r = 30 cm, w= pi/10 per sec and t = 4 sec.

• pi/10

• 2 pi

• 3 pi

• pi/2