Q: A pizza slice has a central angle of $$60^{\circ}$$ and a radius of 8 inches. What is the length of the curved edge of the slice?

$$\dfrac{8\pi}{3}\ \text{inches}$$

Q: Which of the following is the correct formula for the length of an arc intercepted by a central angle $$\theta (in $$degrees) in a circle of radius $$r$$?

$$s = \dfrac{\theta}{360$$^{\circ}$$} \cdot 2\pi r$$

Question 1

A central angle in a circle of radius 5 cm intercepts an arc of length 8 cm. What is the measure of the angle in radians?

Accepted Answer

$$1.6$$

Question 2

Convert $$135^{\circ} to $$radians.

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 3

A Ferris wheel with a radius of 10 meters makes one complete revolution in 40 seconds. What is the linear speed of a seat on the edge of the wheel?

Accepted Answer

$$\dfrac{\pi}{2}\ 	ext{m/s}$$

Question 4

Which of the following best describes a radian?

Accepted Answer

The angle at the center of a circle that intercepts an arc equal in length to the radius

Question 5

A pizza slice has a central angle of $$60^{\circ}$$ and a radius of 8 inches. What is the length of the curved edge of the slice?

Accepted Answer

$$\dfrac{8\pi}{3}\ 	ext{inches}$$

Question 6

A runner completes a circular track of radius 20 meters in 50 seconds. What is the runner’s angular speed in radians per second?

Accepted Answer

$$\dfrac{2\pi}{50}$$

Question 7

Convert $$2.5$$ radians to degrees.

Accepted Answer

$$143.24^{\circ}$$

Question 8

A car tire has a radius of 14 inches. If the tire rotates at 600 revolutions per minute, what is the linear speed of a point on the edge of the tire in inches per minute?

Accepted Answer

$$16,800\pi$$

Question 9

A central angle of $$\dfrac{\pi}{3}$$ radians in a circle of radius 12 cm intercepts an arc. What is the length of the arc?

Accepted Answer

$$4\pi cm$$

Question 10

A boat leaves Gloucester on a bearing of $$155^{\circ}. $$Which of the following best describes this bearing?

Accepted Answer

Measured clockwise from due north

Question 11

If a central angle in a circle of radius $$r$$ intercepts an arc of length $$s$$, what is the formula for the angle in radians?

Accepted Answer

$$	heta = \dfrac{s}{r}$$

Question 12

A circular sector has a radius of 6 cm and a central angle of $$120^{\circ}. $$What is the length of the arc?

Accepted Answer

$$4\pi cm$$

Question 13

Which of the following is the correct formula for the length of an arc intercepted by a central angle $$	heta (in $$degrees) in a circle of radius $$r$$?

Accepted Answer

$$s = \dfrac{	heta}{360$$^{\circ}$$} \cdot 2\pi r$$

Question 14

A wheel of radius 0.5 meters rotates at 120 revolutions per minute. What is the angular speed in radians per second?

Accepted Answer

$$4\pi$$

Question 15

A central angle of $$90^{\circ} in a $$circle of radius 10 cm intercepts an arc. What is the length of the arc?

Accepted Answer

$$5\pi cm$$

Angles and Their Measures: Degrees, Radians, Arc Length, and Motion

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