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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