11.3 Sectors and Arcs Quiz

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Name: ________________________ Class: ___________________ Date: __________ ID: A

11.3 Sectors and Arcs Quiz

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. (1 point) Jenny’s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120°_{. What is the area of Jenny’s slice of cake? Give your answer in terms of}π_.

a. 300π cm2 b. 10π _cm2

c. 150π cm2 d. 3600π _cm2

____ 2. (1 point) Find the arc length of an arc with measure 130° in a circle with radius 2 in. Round to the nearest tenth.

a. 4.5 in b. 2.3 in c. 10.2 in d. 0.5 in

BONUS

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ID: A

11.3 Sectors and Arcs Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: A A=π_r2 m° 360° Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Formula for area of a sector

=π₍₃₀₎2 120° 360°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Substitute the given values.

=₃₀₀π_cm2 Simplify.

Feedback A _Correct!

B _{Use the formula for finding the area of a sector.} C _{Use the formula for finding the area of a sector.}

D _{The area of a sector is equal to pi times radius squared times the measure of the arc}

divided by 360 degrees.

PTS: 1 DIF: Average REF: 1cdc792e-4683-11df-9c7d-001185f0d2ea OBJ: 11-3.2 Application LOC: MTH.C.12.12.02.010

TOP: 11-3 Sector Area and Arc Length KEY: circle | sector area DOK: DOK 2

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ID: A 2. ANS: A L=₂π_r m° 360° Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Formula for arc length

=₂π₍₂₎ 130° 360° Ê Ë ÁÁÁ ˆ_¯˜˜˜ Substitute. = 13 9 π in≈4.5 in Simplify. Feedback A _Correct!

B _{Use the formula for finding the distance along an arc.}

C _{The arc length is equal to 2 times pi times the radius times the measure of the arc}

D _{Use the formula for finding the distance along an arc.}

PTS: 1 DIF: Average REF: 1cdedb8a-4683-11df-9c7d-001185f0d2ea OBJ: 11-3.4 Finding Arc Length LOC: MTH.C.12.11.02.006

TOP: 11-3 Sector Area and Arc Length KEY: arc length DOK: DOK 2

SHORT ANSWER 1. ANS:

10.3 cm2

Step 1 Find the area of sector POM A=π_r2 m°

360°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Formula for area of a sector = π₍₆₎2 90°

360°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Substitute 6 for r and 90 for m. = 9πcm2 Simplify.

Step 2 Find the area of ∆_POM_.

A= 1

2 bh= 1

2(6)(6) OM = 6 cm and h = 6 cm.

A=_{18 cm}2 Simplify.

Step 3 Find the area of segment POM.

area of segment POM = area of sector POM – area of ∆_POM

area of segment POM = 9π_{– 18}≈_{10.3 cm}2

PTS: 2 DIF: Average REF: 1cdca03e-4683-11df-9c7d-001185f0d2ea OBJ: 11-3.3 Finding the Area of a Segment

LOC: MTH.C.12.12.02.004 | MTH.C.12.12.02.010 TOP: 11-3 Sector Area and Arc Length KEY: circle | segment area DOK: DOK 2

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Name: ________________________ Class: ___________________ Date: __________ ID: B

11.3 Sectors and Arcs Quiz

Multiple Choice

a. 2.3 in b. 10.2 in c. 4.5 in d. 0.5 in

____ 2. (1 point) Jenny’s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120°_{. What is the area of Jenny’s slice of cake? Give your answer in terms of}π.

a. 300π cm2 b. 150π _cm2

c. 10π cm2 d. 3600π _cm2

BONUS

1. (2 points) Find the area of segment POM. Round to the nearest tenth.

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ID: B

11.3 Sectors and Arcs Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: C L=₂π_r m° 360° Ê Ë

=₂π(2) 130₃₆₀°° Ê Ë ÁÁÁ ˆ_¯˜˜˜ Substitute. = 13 9 π in≈4.5 in Simplify. Feedback

A _{Use the formula for finding the distance along an arc.}

B _{The arc length is equal to 2 times pi times the radius times the measure of the arc}

C _Correct!

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ID: B 2. ANS: A A=π_r2 m° 360° Ê Ë

=π(30)2Ê120₃₆₀°_°

Ë

=₃₀₀πcm2 Simplify.

Feedback A _Correct!

B _{Use the formula for finding the area of a sector.} C _{Use the formula for finding the area of a sector.}

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ID: B

10.3 cm2

360°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Formula for area of a sector = π(6)2 ₃₆₀90°°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Substitute 6 for r and 90 for m. = 9π_cm2 _Simplify.

A= 1

2 bh= 1

2(6)(6) OM = 6 cm and h = 6 cm.

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Name: ________________________ Class: ___________________ Date: __________ ID: C

11.3 Sectors and Arcs Quiz

Multiple Choice

a. 4.5 in b. 2.3 in c. 10.2 in d. 0.5 in

____ 2. (1 point) Jenny’s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120°_{. What is the area of Jenny’s slice of cake? Give your answer in terms of}π.

a. 10π cm2 b. 150π _cm2

c. 300π cm2 d. 3600π _cm2

BONUS

1. (2 points) Find the area of segment POM. Round to the nearest tenth.

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ID: C

11.3 Sectors and Arcs Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: A L=₂π_r m° 360° Ê Ë

=₂π(2) 130₃₆₀°° Ê Ë ÁÁÁ ˆ_¯˜˜˜ Substitute. = 13 9 π in≈4.5 in Simplify. Feedback A _Correct!

B _{Use the formula for finding the distance along an arc.}

C _{The arc length is equal to 2 times pi times the radius times the measure of the arc}

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ID: C 2. ANS: C A=π_r2 m° 360° Ê Ë

=π(30)2Ê120₃₆₀°_°

Ë

=₃₀₀πcm2 Simplify.

Feedback

A _{Use the formula for finding the area of a sector.} B _{Use the formula for finding the area of a sector.} C _Correct!

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ID: C

10.3 cm2

360°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Formula for area of a sector = π(6)2 ₃₆₀90°°

Ê Ë

ÁÁÁ ˆ_¯˜˜˜ Substitute 6 for r and 90 for m. = 9π_cm2 _Simplify.

A= 1

2 bh= 1

2(6)(6) OM = 6 cm and h = 6 cm.