Q: Which formula gives the area $$A of a $$sector of a circle with radius $$r$$ and central angle $$\theta (in $$radians)?

$$A = \frac{1}{2} r^2$ \theta$$

Question 1

A circular garden has a radius of 10 meters. If a sector of the garden is formed by a central angle of $$\frac{\pi}{3}$$ radians, what is the area of the sector?

Accepted Answer

$$\frac{50\pi}{3}$$

Question 2

A pizza with a radius of 12 inches is sliced into a wedge with a central angle of $$60^\circ. $$What is the length of the crust (arc) of this slice? (Round your answer to two decimal places.)

Accepted Answer

$$8.38$$ inches

Question 3

Which formula gives the area $$A of a $$sector of a circle with radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 4

A circular track has a radius of 50 meters. How far does a runner travel if she runs along an arc subtending a central angle of $$2$$ radians?

Accepted Answer

$$100$$ meters

Question 5

A sector of a circle has an area of $$20$$ square centimeters and a radius of $$4$$ centimeters. What is the central angle in radians?

Accepted Answer

$$2.5$$ radians

Question 6

If the central angle of a sector is given in degrees, what must you do before using the area or arc length formulas?

Accepted Answer

Convert the angle to radians

Question 7

A circular swimming pool has a radius of $$15$$ meters. What is the area of a sector formed by a central angle of $$\frac{\pi}{4}$$ radians?

Accepted Answer

$$\frac{225\pi}{8}$$

Question 8

A clock's minute hand is $$8 cm $$long. How far does the tip of the minute hand travel in $$15$$ minutes?

Accepted Answer

$$4\pi cm$$

Question 9

A sector of a circle has a radius of $$6 cm $$and a central angle of $$120^\circ. $$What is the area of the sector?

Accepted Answer

$$12\pi cm$^2$$

Question 10

A circular field has a radius of $$20$$ meters. If a sector has an arc length of $$15$$ meters, what is the central angle in radians?

Accepted Answer

$$0.75$$ radians

Question 11

Which of the following statements is TRUE regarding the formulas for area and arc length of a sector?

Accepted Answer

Both formulas require the central angle to be in radians

Question 12

A circular park has a radius of $$30$$ meters. What is the length of the arc intercepted by a central angle of $$\frac{\pi}{6}$$ radians?

Accepted Answer

$$5\pi$$ meters

Question 13

A sector of a circle has a radius of $$9 cm $$and a central angle of $$\frac{\pi}{2}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{81\pi}{4}$$

Question 14

A circular racetrack has a radius of $$25$$ meters. If a car travels along an arc with a central angle of $$\frac{\pi}{5}$$ radians, how far does the car travel?

Accepted Answer

$$\frac{25\pi}{5}$$ meters

Question 15

A circular slice of cake has a radius of $$7 cm $$and a central angle of $$45^\circ. $$What is the area of the slice?

Accepted Answer

$$\frac{49\pi}{8}$$

Question 16

A circular fountain has a radius of $$18$$ meters. What is the area of a sector formed by a central angle of $$\frac{\pi}{6}$$ radians?

Accepted Answer

$$\frac{162\pi}{12}$$ meters$$^2$$

Question 17

A circular path has a radius of $$5$$ meters. If a person walks along an arc with a central angle of $$150^\circ$$, how far does the person walk?

Accepted Answer

$$13.09$$ meters

Question 18

A circular sector has a radius of $$10 cm $$and a central angle of $$\frac{\pi}{2}$$ radians. What is the length of the arc?

Accepted Answer

$$5\pi cm$$

Question 19

A circular garden has a radius of $$8$$ meters. If a sector has an area of $$16\pi$$ square meters, what is the central angle in radians?

Accepted Answer

$$0.5$$ radians

Question 20

A circular field has a radius of $$12$$ meters. What is the area of a sector formed by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

$$24\pi$$ meters$$^2$$

Applications of Radian Measure: Area and Arc Length of a Sector

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