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arc length and sector area - Printable Mathematics Worksheets - Wayground

arc length and sector area

20 questions

10th - 10th Grade

Mathematics

This Grade 10 mathematics worksheet gives students focused practice with arc length and sector area. Across 20 items—19 multiple-choice questions and one fill-in-the-blank question—students use circle radius or diameter, central angle, and circumference relationships to calculate arc lengths and the areas of sectors. Problems include shaded sectors, circular tracks, a dog’s range, a pie, a pizza, and an annulus, helping students connect formulas to diagrams and real-world contexts. The worksheet also asks students to identify minor and major arcs, find an unknown radius from a sector area, calculate complementary sector areas, and express answers exactly with π or round them as directed. It is designed for Grade 10 math lessons, guided practice, independent work, homework, or review before an assessment. This free printable worksheet includes a complete answer key so teachers can quickly check students’ calculations and reasoning.

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Worksheets

arc length and sector area

Total questions: 20

Name
Class
Date
1.
Find the arc length.
a)
5.50 cm
b)
11.00 cm
c)
0.39 cm
d)
141.37 cm
2.
Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.
a)
47
b)
74
c)
94
d)
123
3.

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

4.
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.
5.
Find the length of the bold arc.
a)
61.3ft
b)
20.4ft
c)
7351.3ft
d)
22,068ft
6.

Calculate the length of the bold arc.

a)

49.7 ft

b)

15.8 ft

c)

24.9 ft

d)

3.14 ft

7.

Calculate the area of the sector.

a)

4248 m2

b)

7.9 m2

c)

2827.4 m2

d)

11.8 m2

8.
When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.
a)
40
b)
35
c)
55
d)
69
9.

Find the circumference of circle C.

(a)  

10.
Stephanie was jogging around circular track. One part of the track was darker than the rest. She found the angle to be 270 degrees. She found the diameter was thirty feet. What is the arc length around the darker part of the track she jogged on? (rounded to the nearest whole number)
a)
71 feet
b)
141 feet
c)
84 feet
d)
63 feet
11.
Stephanie is cutting a pie. Stephanie's mother wants one fourth of the pie. The diameter is 20 cm. What is the sector area of the pie her mother does not want?
a)
235.62 cm squared
b)
three fourths of the pie
c)
78.54 cm squared
d)
83.99 cm squared
12.
If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?
a)
161.97 mm2
b)
What's Pacman?
c)
39.1 mm2
d)
9.77 mm2
13.

If r = 12 cm and R = 18 cm, what is the exact area of the shaded region in terms of ㄫ?

a)

280ㄫ sq.cm

b)

190ㄫ sq.cm

c)

180ㄫ sq.cm

d)

80ㄫ sq.cm

14.

A 14 -inch pizza was cut into 8 slices. What is the approximate area of one slice of pizza?

a)

9.23 sq. in

b)

19.23 sq. in

c)

19.32 sq. in

d)

20.23 sq. in

15.

Analyze the given figure and solve for the exact area of the

of the annulus.

a)

69π sq. in

b)

36π sq. in

c)

33π sq. in

d)

63π sq. in

16.

Find the area of the shaded region.

a)

6π cm2

b)

60π cm2

c)

36π cm2

d)

64π cm2

17.
Find the area of a parallelogram with a base of 30 m and a height of 25 m
a)
750 m2
b)
375 m2
c)
705 m2
d)
110 m2
18.
Find the area
a)
25 yd2
b)
20 yd2
c)
30yd2
d)
25.5yd2
19.
Find the area of the triangle.
a)
39 sq feet
b)
30.8 sq feet
c)
78 sq feet
d)
101.4 sq feet
20.
area?
a)
108 cm sq
b)
60 cm
c)
432 cm sq
d)
216 cm sq
Answer Key

arc length and sector area

Total questions: 20

1.
b) 11.00 cm
2.
c) 94
3.
a)

16 in

4.
c) 31.4 sq. in.
5.
a) 61.3ft
6.
a)

49.7 ft

7.
d)

11.8 m2

8.
d) 69
9.
37.71, 37.7, 37, 38
10.
a) 71 feet
11.
a) 235.62 cm squared
12.
a) 161.97 mm2
13.
c)

180ㄫ sq.cm

14.
b)

19.23 sq. in

15.
d)

63π sq. in

16.
b)

60π cm2

17.
a) 750 m2
18.
a) 25 yd2
19.
a) 39 sq feet
20.
d) 216 cm sq

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FAQs

What does this arc length and sector area worksheet cover?

This Grade 10 worksheet practices calculating arc lengths and sector areas from a circle’s radius or diameter and central angle. Its 19 multiple-choice and one fill-in-the-blank items include shaded sectors, major and minor arcs, complementary regions, circumference, and an annulus, with students sometimes rounding and sometimes keeping answers in terms of π.

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

Introduce the arc-length and sector-area formulas by connecting each fraction of a circle to its central angle, then model how to substitute a radius or convert a diameter before calculating. Use the worksheet’s track, dog-range, pie, and pizza contexts for guided discussion, asking students to explain why a larger angle produces a longer arc or larger sector and when a complementary region must be used.

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

Watch for students using the diameter where the formula requires the radius, treating a sector angle as a full 360° circle, or choosing the requested sector instead of its complement, as in the pie and Pac-Man problems. Students may also confuse arc length with sector area, round when an exact answer in terms of π is requested, or fail to apply the stated rounding direction.

How do I assign and grade this arc length and sector area worksheet?

On Wayground, this worksheet is available as a printable PDF and as a digital quiz. It includes a complete answer key for the 20 questions, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

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 circle diagrams, angle measures, and calculation choices are easier to follow. You can also select a dyslexia-friendly font or translate the worksheet into another language while students work through the arc-length and sector-area items.

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, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more worksheets at https://wayground.com/en-us/worksheets.

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