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

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

Q: Which of the following is the correct conversion from degrees to radians?

$$\theta_{\text{radians}} = \theta_{\text{degrees}} \times \dfrac{\pi}{180}$$

Q: Which of the following is NOT a necessary condition for using the sector area formula $$A = \dfrac{1}{2} r^2$ \theta$$?

The angle $$\theta$$ must be in degrees.

Question 1

A pizza has a radius of 12 inches. If a slice makes a central angle of $$60^	ext{o}$$, what is the area of the slice? (Round your answer to two decimal places.)

Accepted Answer

$$37.70$$ square inches

Question 2

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

Accepted Answer

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

Question 3

A circular garden has a radius of $$8$$ meters. What is the length of the arc intercepted by a central angle of $$135^	ext{o}$$?

Accepted Answer

$$18.85$$ meters

Question 4

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

Accepted Answer

Convert the angle to radians

Question 5

A sector of a circle has an area of $$10$$ square units and a radius of $$4$$ units. What is the measure of the central angle in radians?

Accepted Answer

$$1.25$$ radians

Question 6

Which of the following statements is TRUE about the formula $$s = r 	heta$$ for arc length?

Accepted Answer

It is only valid if $$	heta is in $$radians.

Question 7

A circular track has a radius of $$20$$ meters. How far does a runner travel if she runs along an arc with a central angle of $$\dfrac{\pi}{3}$$ radians?

Accepted Answer

$$20.94$$ meters

Question 8

If a sector of a circle has a central angle of $$\dfrac{\pi}{2}$$ radians and a radius of $$5$$ units, what is the area of the sector?

Accepted Answer

$$12.5$$ square units

Question 9

A clock's minute hand is $$7 cm $$long. What is the distance traveled by the tip of the minute hand in $$20$$ minutes?

Accepted Answer

$$14.66 cm$$

Question 10

Which of the following is the correct conversion from degrees to radians?

Accepted Answer

$$	heta_{	ext{radians}} = 	heta_{	ext{degrees}} 	imes \dfrac{\pi}{180}$$

Question 11

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

Accepted Answer

$$20 cm$$

Question 12

A slice of pie has an area of $$8$$ square inches and was cut from a pie with a radius of $$6$$ inches. What was the central angle of the slice in radians?

Accepted Answer

$$0.44$$ radians

Question 13

If the central angle of a sector is $$\dfrac{\pi}{4}$$ radians and the radius is $$3$$ units, what is the area of the sector?

Accepted Answer

$$2.25$$ square units

Question 14

A circular fountain has a radius of $$15$$ meters. What is the area of a sector formed by a central angle of $$120^	ext{o}$$?

Accepted Answer

$$235.62$$ square meters

Question 15

A sector of a circle has a central angle of $$\dfrac{\pi}{6}$$ radians and a radius of $$9$$ units. What is the arc length?

Accepted Answer

$$4.71$$ units

Question 16

Which of the following is NOT a necessary condition for using the sector area formula $$A = \dfrac{1}{2} r^2$ 	heta$$?

Accepted Answer

The angle $$	heta$$ must be in degrees.

Question 17

A circular park has a radius of $$25$$ meters. What is the length of the arc intercepted by a central angle of $$45^	ext{o}$$?

Accepted Answer

$$19.63$$ meters

Question 18

A sector of a circle has an area of $$20$$ square units and a central angle of $$\dfrac{\pi}{3}$$ radians. What is the radius of the circle?

Accepted Answer

$$6.18$$ units

Question 19

A circular slice has a radius of $$10 cm $$and a central angle of $$90^	ext{o}. $$What is the arc length?

Accepted Answer

$$15.71 cm$$

Question 20

A circular garden has a radius of $$5$$ meters. What is the area of a sector with a central angle of $$270^	ext{o}$$?

Accepted Answer

$$18.75$$ square meters

Area and Arc Length of a Sector of a Circle

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