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Area of a sector of a circle - Printable Mathematics Worksheets - Wayground

Area of a sector of a circle

11 questions

9th - 9th Grade

Mathematics

Area of a Sector of a Circle is a Grade 9 mathematics worksheet that builds foundational understanding of sectors, central angles, arcs, and circle-area relationships. Students identify the vertex of a central angle, connect arc length with circumference, recognize that a sector represents part of a circle, and use degrees and radians to describe angles. The worksheet includes 11 questions: one fill-in-the-blank item and 10 multiple-choice questions. Students apply the sector-area formula to find areas for specific radii and central angles, including 90°, 60°, and 180° sectors, and work backward from a sector area to determine the area of the full circle. This free printable worksheet includes a complete answer key and is designed for Grade 9 math practice, review, or formative assessment.

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Area of a sector of a circle

Total questions: 11

Name
Class
Date
1.

The Radius of a circle is (a)   it's diameter.

2.

The central angle of an arc of a circle has its ______ at the center of the circle.

a)

segment

b)

vertex

c)

acute

d)

end point

3.

The area of a circle is given by the formula Pi times _____

a)

Radius

b)

diamater

c)

diameter square

d)

radius square

4.

The length of an arc of a circle is related to the _______ of the circle.

a)

Diameter

b)

Area

c)

Angle

d)

Circumference

5.

The area of a sector of a circle is related to the _______ of the circle.

a)

circumference

b)

radius

c)

area

d)

length

6.

A sector of a circle looks similar to a _____

a)

Cone

b)

Plate

c)

Slice of pizza

d)

burger

7.

A sector of a circle has a central angle of 90 degrees and radius 1 cm. The area of the sector is ____sq.cm

a)

pi

b)

2pi

c)

pi/4

d)

pi/8

8.

A circle has a radius of 6 cm. A sector subtends an angle of 60 degrees at the center. The area of this sector is _____ sq cm

a)

36

b)

6

c)

6pi

d)

pi

9.

An angle can be measured in _______ and _____.

a)

cm and,

b)

feet , inches

c)

degrees , radians

d)

decimals, integers

10.

The area of a sector making an angle of 180 degrees is 28 sq. units. The area of the circle must be ____ sq units.

a)

10

b)

14

c)

56

d)

112

11.

The central angle of an arc of a circle has its ______ at the center of the circle.

a)

segment

b)

vertex

c)

acute

d)

end point

Answer Key

Area of a sector of a circle

Total questions: 11

1.
Half
2.
b)

vertex

3.
d)

radius square

4.
d)

Circumference

5.
c)

area

6.
c)

Slice of pizza

7.
c)

pi/4

8.
c)

6pi

9.
c)

degrees , radians

10.
c)

56

11.
b)

vertex

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FAQs

What does this Area of a Sector of a Circle worksheet cover?

This Grade 9 worksheet combines vocabulary and calculation practice for finding the area of a sector from its radius and central angle. Its 11 items include one fill-in-the-blank question and 10 multiple-choice questions covering central-angle vertices, radius relationships, circle area, angle units, and sector areas such as 90°, 60°, and 180°.

How can I use this worksheet to teach area of a sector?

Introduce a sector as a fraction of a circle, using the worksheet’s pizza-slice comparison before presenting the sector-area formula. Model how the central angle determines the fraction of the full circle, then have students solve the 90° and 60° examples by substituting the radius and angle. Use the 180° item to discuss working backward from a sector area to the area of the complete circle.

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

Watch for students using the radius instead of radius squared in the circle-area formula, or confusing circumference with area when interpreting the arc and sector questions. Students may also identify an endpoint rather than the vertex of a central angle, treat a 60° or 90° sector as a full circle, or overlook that a 180° sector represents half of the circle. Check that they distinguish degrees from radians when identifying angle units.

How do I assign and grade this Area of a Sector of a Circle worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the fill-in-the-blank and multiple-choice items for independent practice, review, or assessment. 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 classrooms that are reducing screen time.

How can I differentiate this sector-area worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the formula-based questions and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language. These options can make the central-angle vocabulary and sector-area calculations more accessible without changing the questions.

Where can I find more free 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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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