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Arc Length and Sector Area - Printable Mathematics Worksheets class 9 - Wayground

Arc Length and Sector Area

20 questions

9th - 12th Grade

Mathematics

Arc Length and Sector Area is a free printable Mathematics worksheet for students in Grades 9–12. It develops fluency with circle circumference, arc length, and sector area by asking students to select valid formulas, calculate measurements from given circle information, identify circumference, and solve shaded-sector problems. Students work with exact answers in terms of π, decimal approximations, and specified rounding directions. The 20-question worksheet combines 2 multiple-select questions, 14 multiple-choice questions, and 4 matching items. It gives students practice choosing between circumference and arc-length formulas, matching calculated results, converting exact values to decimals when prompted, and finding sector areas from radius and central-angle information. The worksheet includes a complete answer key, making it useful for guided practice, independent review, homework, or a standards-aligned assessment of circle measurement skills.

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Arc Length and Sector Area

Total questions: 20

Name
Class
Date
1.

Which of the following can be used to calculate the circumference of a circle? (SELECT ALL THAT APPLY)

a)

C=2πrC=2\pi r

b)

C=πr2C=\pi r^2

c)

A = πr2A\ =\ \pi r^2

d)

C=πdC=\pi d

2.

Calculate the circumference, 2πr2\pi r , of the circle. (Leave answers in terms of π\pi . Do not round your answer.)

a)

4π4\pi m

b)

1π1\pi m

c)

2π2\pi m

3.

Calculate the circumference, 2πr2\pi r , of of the circle. (Leave answers in terms of π\pi . Do not round your answer.)

a)

3π3\pi yd

b)

12π12\pi yd

c)

6π6\pi yd

4.

Calculate the circumference of the circle. (Leave answers in terms of π\pi . Do not round your answer.)

a)

3π3\pi km

b)

6π6\pi km

c)

2π2\pi km

5.

Which of the following formulas calculates the arc length of a circle? (Select ALL that apply.)

a)

θ180×2πr\frac{\theta}{180}\times2\pi r

b)

θ360×2πr\frac{\theta}{360}\times2\pi r

c)

θ360×πd\frac{\theta}{360}\times\pi d

d)

θ360×πr2\frac{\theta}{360}\times\pi r^2

6.

Find the arc length of the circle. (Leave answers in terms of π\pi . Do not round your answer.)

a)

27π27\pi km

b)

π18\frac{\pi}{18} km

c)

15π15\pi km

d)

15π2\frac{15\pi}{2}

7.

Find the arc length of the circle. (Leave answers in terms of π\pi . Do not round your answer.)

a)

27π27\pi km

b)

π18\frac{\pi}{18} km

c)

15π15\pi km

d)

45π2\frac{45\pi}{2} km

8.

Find the arc length of the circle. (Round your answer to the nearest tenth.)

a)

42.4 m

b)

21.2 m

c)

84.8 m

d)

6.7 m

9.
Question Image

Match the answers to the following problems.

3π3\pi

Problem 1

21π2\frac{21\pi}{2}

Problem 4

5π5\pi

Problem 3

289π12\frac{289\pi}{12}

Problem 2

10.
Question Image

Match the answers to the following problems. (HINT: change your answer to decimal)

20.4

Problem 1

47.1

Problem 4

5.2

Problem 3

18.8

Problem 2

11.

What is this called?

a)

Chord

b)

Minor Arc

c)

Circumference

d)

Secant

12.

What is the circumference, in inches, of a circle with a radius of 8 inches?

a)

4π

b)

8π

c)

12π

d)

16π

e)

64π

13.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer as an exact value

a)

5π/3

b)

10π/3

c)

10π

d)

40π

14.

What is the area of the shaded region? Round to the nearest hundredth.

a)

8π/3

b)

2π/3

c)

32π/3

d)

4π/3

15.

What is the area of the shaded sector?

a)

221π/36

b)

3757π/72

c)

3757π/18

d)

None of these

16.

What is the area of the shaded sector?

a)

40π/9

b)

400π/9

c)

80π/9

d)

1600π/9

17.

Match the following formulas.

 2π(r)\ 2\pi\left(r\right)

Circumference

 π(r)2\ \pi\left(r\right)^2

Area

 2π(r)(θ)360°\ \frac{2\pi\left(r\right)\left(\theta\right)}{360\degree}

Arc Length

 π(r)2(θ)360°\ \frac{\pi\left(r\right)^2\left(\theta\right)}{360\degree}

Area of Sector

18.

Match the following

The distance around the circle.

Circumference

The amount of space inside the circle.

Area

The distance around a section of the circle.

Arc Length

The amount of space inside a section of the circle.

Area of a Sector

19.

What is the green area called?

a)

Sector

b)

Circumference

c)

Arc Length

d)

Area

20.

Find exact length of the un-shaded part of the circle.

a)

6π cm6\pi\ cm

b)

8π cm8\pi\ cm

c)

2π cm2\pi\ cm

d)

4π cm4\pi\ cm

Answer Key

Arc Length and Sector Area

Total questions: 20

1.
a)

C=2πrC=2\pi r

, d)

C=πdC=\pi d

2.
a)

4π4\pi m

3.
b)

12π12\pi yd

4.
b)

6π6\pi km

5.
b)

θ360×2πr\frac{\theta}{360}\times2\pi r

, c)

θ360×πd\frac{\theta}{360}\times\pi d

6.
c)

15π15\pi km

7.
d)

45π2\frac{45\pi}{2} km

8.
a)

42.4 m

9.

3π3\pi

 - 

Problem 1

, 

21π2\frac{21\pi}{2}

 - 

Problem 4

, 

5π5\pi

 - 

Problem 3

, 

289π12\frac{289\pi}{12}

 - 

Problem 2

10.

20.4

 - 

Problem 1

, 

47.1

 - 

Problem 4

, 

5.2

 - 

Problem 3

, 

18.8

 - 

Problem 2

11.
c)

Circumference

12.
d)

16π

13.
c)

10π

14.
a)

8π/3

15.
b)

3757π/72

16.
d)

1600π/9

17.

 2π(r)\ 2\pi\left(r\right)

 - 

Circumference

, 

 π(r)2\ \pi\left(r\right)^2

 - 

Area

, 

 2π(r)(θ)360°\ \frac{2\pi\left(r\right)\left(\theta\right)}{360\degree}

 - 

Arc Length

, 

 π(r)2(θ)360°\ \frac{\pi\left(r\right)^2\left(\theta\right)}{360\degree}

 - 

Area of Sector

18.

The distance around the circle.

 - 

Circumference

, 

The amount of space inside the circle.

 - 

Area

, 

The distance around a section of the circle.

 - 

Arc Length

, 

The amount of space inside a section of the circle.

 - 

Area of a Sector

19.
a)

Sector

20.
d)

4π cm4\pi\ cm

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FAQs

What does the Arc Length and Sector Area worksheet cover?

This Grade 9–12 Mathematics worksheet covers calculating circle circumference, arc length, and shaded sector area. Its 20 items use multiple-select, multiple-choice, and matching formats to have students choose valid formulas, calculate exact values in terms of π, round selected answers, and match circle-measurement results.

How can I use this worksheet to teach circumference, arc length, and sector area?

Introduce the worksheet by reviewing how radius and diameter connect to circumference, then model how a fraction of a circle’s circumference represents an arc length and how a central angle determines a sector’s area. Have students explain why each formula applies before completing the multiple-choice and matching items, and use the exact-versus-rounded prompts to discuss when π should remain in the answer or be converted to a decimal.

What mistakes should I watch for when students complete this circle-measurement worksheet?

Watch for students using the radius where the circumference formula requires a diameter, or using a full circumference formula without accounting for the arc’s central-angle fraction. Students may also select only one answer on the multiple-select formula questions, confuse circumference with a chord or minor arc, or round answers that explicitly must remain in terms of π.

How do I assign and grade the Arc Length and Sector Area worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also supports schools that are reducing screen time while keeping practice available.

How can I differentiate this circumference, arc length, and sector area worksheet?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the formula-selection, calculation, and matching items are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when that supports access to the circle-measurement instructions and answer choices.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, including downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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