Wayground
Arc Length and Sector Area Word Problems - Printable Mathematics Worksheets - Wayground

Arc Length and Sector Area Word Problems

15 questions

10th Grade

Mathematics

Arc Length and Sector Area Word Problems is a free printable Grade 10 mathematics worksheet for practicing how to calculate arc lengths, sector areas, and shaded regions in circles. Students work with central angles given in degrees and radians, apply circle formulas, identify valid arc-length formulas, and solve for a circle’s radius from a sector area. Several problems require exact answers, while others require decimal answers rounded to a specified place. The 15-question set uses 13 multiple-choice questions, one multiple-select formula question, and one matching item. Diagrams and word problems ask students to distinguish arc length from sector area, use the radius and central angle correctly, and match calculated results after converting to decimals. It is designed for Grade 10 math practice, independent review, homework, or formative assessment, and includes a complete answer key for checking student work.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Arc Length and Sector Area Word Problems

Total questions: 15

Name
Class
Date
1.

FIND THE ARC LENGTH OF THE BOLDED ARC

a)

A

b)

B

c)

C

d)

D

2.

Given that m∠AOB = 13π/18 and the radius is 8 cm, what is the length of arc AB?

a)

13π/8 cm

b)

52π/9 cm

c)

π/9 cm

d)

9π/52

3.

What is the area of sector​ GPH?

a)

9π yd2

b)

32π yd2

c)

18π yd2

d)

6π yd2

4.

Find the area of the shaded sector of the circle.

a)
b)
c)
d)
5.

In a​ circle, a 90° sector has area 64π in2. What is the radius of the​ circle?

a)

16 in

b)

32 in

c)

64 in

d)

128 in

6.

Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

7.

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

a)

26

b)

452.39

c)

113.10

d)

40715.04

8.

Find the arc length of the circle. (Leave answers in terms of . 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

9.

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

10.

What is the area of the shaded sector?

a)

40π/9

b)

400π/9

c)

80π/9

d)

1600π/9

11.

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

12.

Find the arc length of the circle. (Leave answers in terms of . 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}

13.
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

14.

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

15.

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

Answer Key

Arc Length and Sector Area Word Problems

Total questions: 15

1.
d)

D

2.
b)

52π/9 cm

3.
a)

9π yd2

4.
b)
5.
a)

16 in

6.
c)

31.4 sq. in.

7.
c)

113.10

8.
d)

45π2\frac{45\pi}{2} km

9.
a)

42.4 m

10.
d)

1600π/9

11.
b)

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

, c)

θ360×πd\frac{\theta}{360}\times\pi d

12.
c)

15π15\pi km

13.

20.4

 - 

Problem 1

, 

47.1

 - 

Problem 4

, 

5.2

 - 

Problem 3

, 

18.8

 - 

Problem 2

14.
c)

10π

15.
a)

8π/3

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Arc Length and Sector Area Word Problems worksheet cover?

This Grade 10 worksheet builds fluency with calculating arc lengths, sector areas, and shaded regions using a circle’s radius and central angle. Its 15 items combine multiple-choice diagrams and word problems with a multiple-select question about arc-length formulas and a matching task that requires converting results to decimals. Students also practice deciding when to leave an answer exact and when to round it.

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

Introduce the worksheet by having students compare the formulas for a fraction of a circumference and a fraction of a circle’s area, then discuss how the central angle determines that fraction. Model one degree-based example and one radian-based example before assigning the multiple-choice shaded-sector problems. Use the formula-selection item and matching question as discussion checkpoints, asking students to explain why an answer represents a length rather than an area.

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

Students may use the sector-area formula for an arc-length question, substitute the diameter instead of the radius, or fail to convert a degree measure into the appropriate fraction of a full circle. They may also round when an exact answer is requested, leave a decimal unrounded when a place value is specified, or match a correct calculation to the wrong decimal in the final matching item. Check that students attach linear units to arc lengths and square units to sector areas.

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

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for the 15 questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital quiz can be assigned through Wayground for online response collection and grading.

How can I differentiate this arc length and sector area worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the multiple-choice choices, circle diagrams, and matching items are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet’s directions and question text into another language while students continue working with the same arc-length and sector-area calculations.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion