circle problem solving worksheet

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• Circumference and Area

Circumference and Area of a Circle Worksheets

This page is a one-stop shop for all your finding area and circumference of a circle exercises. Catering to the learning needs of students in grade 5 through grade 8, these printable worksheets practice the topic pretty much across the board: easy, moderate and hard. The job in the easy set is to calculate the area and circumference of the circles with radius ranging from 1 to 25. The moderate set requires rounding answers to tenth place with the radius of circles ranging between 25 and 100. In the hard worksheets, the radius is rendered in decimal and the task is to round your answers to two decimal places. Use pi = 3.14 wherever necessary. Explore some of these worksheets for free!

Area from Radius

Applying the formula, Area = pi * r 2 , find the area of each circle.

• Download the set

Area from Diameter

Find the radius from diameter and apply the formula to find the area of a circle.

Area from Radius or Diameter

Each printable worksheet has 9 problems on finding area of a circle with the known radius or diameter. Two simple word problems and one story problem included.

Area and Circumference: Combined Review

These are the perfect review worksheets in finding both area and circumference of the circle.

Radius or Diameter from Area

Dividing the area by pi or 3.14, you get r 2 . Taking the square root, you get radius. Solve each problem based on this technique.

Area from Circumference

Find the area from the circumference of each circle in this stock of worksheets for 7th grade students. Word problems included to understand real-life application.

Circumference from Radius

Applying the formula, Circumference = 2 * pi * r, find the circumference of each circle.

Circumference from Diameter

To find the circumference, multiply diameter with pi value. Each pdf worksheet has 9 problems.

Circumference from Radius or Diameter

Circumference of a circle worksheet contains six standard problems and two word problems.

Radius or Diameter from Circumference

Divide the circumference by pi or 3.14. You get the diameter. Answer the questions.

Circumference from Area

Each worksheet has 8 problems finding circumference from area of a circle. Simple word problems included.

Area of an Annulus Worksheets

Imagine two circles with different radii, but the same center; can you calculate the area of the region in between? Scout around these pdf worksheets, pore over the examples, and solve similar problems on area of an annulus!

(9 Worksheets)

Related Worksheets

» Arc Length and Area of Sector

» Area of Segment

» Area of Compound Shapes

» Area of Mixed Shapes

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Circles Worksheets

Circles worksheets help students to get a good understanding of all concepts related to a circle. These can include questions on identifying the radius and diameter of a given circle, calculating the circumference and the area, arcs, central angles, semi-circles and so on.

Benefits of Circles Worksheets

Circles form an integral part of geometry. They are also an important part of several real-life problems. As it is such a vast topic, it can tend to get confusing. Using the circles worksheets helps students to practice multiple questions allowing them to have clear concepts and combat any confusion that they may have.

As these math worksheets provide flexibility, they strengthen each concept under the topic of circles and move to either tougher questions on the same or an entirely different concept.

Download Circles Worksheet PDFs

The worksheets have visual simulations and are interactive to improve a student's learning curve. They are also created in a manner that they are easy to use.

Visual maths worksheets, each maths worksheet is differentiated and visual.

KS3 and KS4 Circle Worksheets

Maths Worksheets / KS3 and KS4 Circle Worksheets

Cazoom Maths has provided a variety of Circle Worksheets covering concepts like  area of circles, circle circumference, arc lengths , and many more, with everything your student or child will need to learn when studying circles. Our circle worksheets will strengthen students’ understanding of the circle theorem. Clear and engaging, our circle theorems worksheets cover topics such a how to calculate the area of a circle, finding the radius and diameter, and calculating circumference, providing valuable practice for students from Year 8 to Year 11. Prepare for GCSE exams and beyond by exploring practical applications and mastering advanced concepts. Each circles worksheet also comes with with answers. At Cazoom Maths we cater to all abilities; therefore you will find a circles worksheet suitable for all students. 

Circle Investigation – Discovering Pi

Area and Circumference

Area of Circles

Circle Area Problems

Circumference

In Terms of Pi (A)

Area of Sectors and Arc Lengths

Circle Theorems (A)

Circle Theorems (B)

Circle Theorems (C)

Finding the Radius or Diameter

In Terms of Pi (B)

Learning the Circle Theorems

The Formulae for Area of Sectors and Arc Lengths

Area of Sectors and Segments

Area of Sectors and Segments (With Clues)

In Terms of Pi (C)

Introducing Radians

Proving Circle Theorems – Angle at the Centre

Proving Circle Theorems – Cyclic Quadrilaterals

PRINTABLE PDF KS3 AND KS4 CIRCLES WORKSHEETS WITH ANSWERS

Empower your child or student with our circle worksheets at Cazoom Maths. From basic concepts to practical applications, our engaging materials cater to all abilities, building confidence and critical thinking skills. With Cazoom Maths worksheets, your students can explore the relevance of circles in real-world scenarios and lay a strong foundation for their GCSE maths examinations.

The Importance of Learning Circle Geometry for Students

Learning about circles by working on these circle worksheets offers numerous benefits for students, extending beyond mathematics. Let’s explore how mastering circle theorems is an integral part of any student’s mathematical studies: 

Critical Thinking Skills:  Analyzing and applying circle properties enhances cognitive skills that are valuable in various subjects and real-life situations.

Interdisciplinary Connections:  Understanding circle theorems establishes connections between mathematics and other disciplines. 

Enhanced Spatial Reasoning:  Delving into circles requires visualizing and manipulating shapes in 2D and 3D spaces, improving spatial reasoning skills for geometry and beyond.

Analytical Mindset: Circle theorems nurture an analytical mindset, encouraging students to break down complex challenges into manageable parts, an invaluable skill throughout their academic and professional endeavours.

Understanding Circle Theorems

At Cazoom Maths Worksheets we are dedicated to providing fun and engaging KS3 and KS4 maths worksheets to save you hours of lesson planning time. With our printable PDF Circle Worksheets students can explore concepts like the angle sum of a circle, properties of chords and tangents, and much more. 

These circle worksheets offer practical insights into real-world applications of circle theorems and enhance your students’ problem-solving skills.

Use of Circles in Real Life: Worksheets to Master Circle Theorems

Circle geometry is all around us! In particular, those who decide to work in the science and architecture industries will use their circle theorem knowledge skills daily. From architecture to everyday designs, circles shape our surroundings. Familiarizing your child or pupil with circle theorems nurtures valuable problem-solving skills, applicable in diverse fields.

Circles in Real Life 

Cazoom Maths Worksheets will teach your child understand the relevance of circles in everyday life, from circular buildings and roundabouts to artistic creations and engineering marvels! Understanding circle theorems equips your child or pupil with essential problem-solving abilities related to this concept and its practical applications.

Explore our engaging circle worksheets, designed to foster a deeper understanding of circle concepts. With a focus on mastering circle theorems, your child or pupil can confidently tackle challenges and excel academically.

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Circles: Radius, Diameter, Circumference, Area

Print out these worksheets on circles.  Practice naming circles and calculating circumference, radius, diameter, and area of a circle.

Circumference and Area (Intermediate)

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Unit 14: Circles

About this unit.

Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.

Circle basics

• Circles glossary (Opens a modal)
• Radius, diameter, circumference & π (Opens a modal)
• Proof: all circles are similar (Opens a modal)

Arc measure

• Intro to arc measure (Opens a modal)
• Finding arc measures (Opens a modal)
• Finding arc measures with equations (Opens a modal)
• Arc measure 4 questions Practice
• Arc measure with equations 4 questions Practice

Arc length (from degrees)

• Arc length from subtended angle (Opens a modal)
• Subtended angle from arc length (Opens a modal)
• Challenge problems: Arc length 1 (Opens a modal)
• Challenge problems: Arc length 2 (Opens a modal)
• Arc length 4 questions Practice

Introduction to radians

• Intro to radians (Opens a modal)
• Radians & degrees (Opens a modal)
• Degrees to radians (Opens a modal)
• Radians to degrees (Opens a modal)
• Radians & degrees 4 questions Practice

Arc length (from radians)

• Arc length as fraction of circumference (Opens a modal)
• Arc length from subtended angle: radians (Opens a modal)
• Challenge problems: Arc length (radians) 1 (Opens a modal)
• Challenge problems: Arc length (radians) 2 (Opens a modal)
• Radians & arc length 4 questions Practice
• Area of a sector (Opens a modal)
• Area of a sector 4 questions Practice

Inscribed angles

• Inscribed angles (Opens a modal)
• Challenge problems: Inscribed angles (Opens a modal)
• Inscribed angle theorem proof (Opens a modal)
• Inscribed angles 4 questions Practice

Inscribed shapes problem solving

• Proof: Right triangles inscribed in circles (Opens a modal)
• Inscribed shapes: find diameter (Opens a modal)
• Inscribed shapes: angle subtended by diameter (Opens a modal)
• Inscribed shapes: find inscribed angle (Opens a modal)
• Challenge problems: Inscribed shapes (Opens a modal)
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• Inscribed quadrilaterals 5 questions Practice

Properties of tangents

• Proof: Radius is perpendicular to tangent line (Opens a modal)
• Determining tangent lines: angles (Opens a modal)
• Determining tangent lines: lengths (Opens a modal)
• Proof: Segments tangent to circle from outside point are congruent (Opens a modal)
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• Tangents of circles problem (example 2) (Opens a modal)
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Area of inscribed triangle

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Standard equation of a circle

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• Features of a circle from its standard equation 4 questions Practice
• Graph a circle from its standard equation 4 questions Practice
• Write standard equation of a circle 4 questions Practice

Expanded equation of a circle

• Features of a circle from its expanded equation (Opens a modal)
• Circle equation review (Opens a modal)
• Features of a circle from its expanded equation 4 questions Practice
• Graph a circle from its expanded equation 4 questions Practice

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Area of a Circle Support Page

Welcome to our Area of a Circle page. Here you will find a range of free printable area sheets and support, which will help your child to learn to work out the area of different circles.

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Area of a Circle

On this webpage you will find our range of worksheets to help your child learn to work out the area of a range of circles.

These sheets are graded from easiest to hardest, and each sheet comes complete with answers.

Using these sheets will help your child to:

• understand what area is;
• know how to find the area of a circle;
• solve word problems involving area of circles;

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

Quicklinks to ...

• What is area?

How to find the Area of a Circle

• Area of a Circle Calculator

Area of a Circle Worksheets

Area of a circle word problems.

• More recommended resources

Area of a Circle Online Quiz

What is area.

• Area is a measure of the amount of space inside a shape.
• It is measured in squares, so it can be square inches (in 2 ), square cm (cm 2 ), square feet(ft 2 ), etc.

The formula for the area of a circle is: A = πr 2 , where r is the radius of the circle.

To find the area of a circle, follow these simple steps:

• find the radius of the circle (the distance from one side to the center of the circle). It is the same as half of the diameter of the circle.
• square the radius (multiply the radius by itself)
• multiply this amount by pi (π)
• you have now found the area of the circle.
• the formula for the circumference of a circle is A = π x r x r or A = π r 2 , where A is the area and r is the radius of the circle.

Pi (written π) is a special mathematical number which is used to help calculate areas and perimeters of circles.

Pi always has the same value which is 3.141592...

Area of a Circle Examples

Area of a circle example 1.

Find the area of the circle below to 1 decimal place.

To find the area of the circle, we need to find the radius first.

The radius is half of the diameter, so it is half of 5 = 2.5 cm.

Next we need to square the radius: 2.5 2 = 2.5 x 2.5 = 6.25 cm.

Finally we need to multiply this amount by pi (π).

So the area of this circle is π x r 2 = π x 6.25 cm.

If we take pi = 3.14, this gives us an area of 3.14 x 6.25 = 19.6 square cm or 19.6 cm 2 to 1 decimal place.

Area of a Circle Example 2

Find the area of the circle below to the nearest inch.

To find the area of a circle, we need to find the radius first.

The radius of the circle is half of the diamter which is half of 7 = 3.5 inches.

Next we need to square the radius: 3.5 2 = 3.5 x 3.5 = 12.25 cm.

So the area of this circle is π x r 2 = π x 12.25 cm.

If we take pi = 3.14, this gives us an area of 3.14 x 12.25 = 38.5 square inches or 38.5 in 2 to 1 decimal place.

Area of a Circle Example 3

Find the area of the circle below and give your answer to the nearest whole number.

To find the area of a circle, we need to square the radius and multiply this by pi (π)

The radius of the circle is 12m, so the square of the radius is 12 2 = 12 x 12 = 144.

So the area of this circle is π x r 2 = π x 144 m.

This gives us an area of π x 144 = 452 square m or 452 m 2 to the nearest whole number.

Our Area of a Circle Calculator will find the area of any circle, if you type in a radius or diameter.

It will take whole numbers, fractions or decimal values.

The best thing about it is that it shows the working out, step-by-step.

We have split the worksheets into 2 different sections:

• This section contains straightforward area of circle questions;
• Each worksheet comes with two versions: version A is in standard units, version B is in metric units.

Sheets 1A and 1B contain circles with the radius marked.

Sheets 2A and 2B contain circles with the diameter marked.

Sheets 3A and 3B contain a mixture of circles with either the diameter or the radius marked.

• Area of a Circle Sheet 1A
• PDF version
• Area of a Circle Sheet 1B (metric version)
• Area of a Circle Sheet 2A
• Area of a Circle Sheet 2B (metric version)
• Area of a Circle Sheet 3A
• Area of a Circle Sheet 3B (metric version)

Sheets 1A and 1B contain straightforward area word problems.

Sheets 2A and 2B contain slightly harder word problems.

Sheets 3A and 3B are the hardest sheets and require multiple steps involving subtracting the areas of circles to find the areas of more complex shapes.

• Area of a Circle Word Problems 1A
• Area of a Circle Word Problems 1B (metric version)
• Area of a Circle Word Problems 2A
• Area of a Circle Word Problems 2B (metric version)
• Area of a Circle Word Problems 3A (harder)
• Area of a Circle Word Problems 3B (harder - metric version)

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Circle Worksheets

• Area of a Semi-Circle

• Area of 1/4 Circle Support

• Area of a 3/4 Circle Support
• Square Inside a Circle Area Support Page
• Perimeter of a Circle
• Perimeter of a Semi-Circle

More Area Support and Resources

We have a range of other area worksheets and support pages for a range of different 2d shapes.

• Area of Rectangle Worksheets
• Area and Perimeter of Rectangle Worksheets
• Area of Right Triangle
• Area of Equilateral Triangle
• Area of Quadrilaterals Worksheets

More Perimeter Worksheets

Here is our selection of free printable perimeter worksheets for 3rd and up.

• Perimeter Worksheets Hub Page

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Word Problems That Involve Circles

Related Topics & Worksheets: Circle Word Problems Worksheet 2 Circle Worksheet Circles

Objective: I know how to evaluate word problems that involve circles.

Evaluate the following word problems. (Take π = 3.14 and round to the nearest hundredths) 1) Find the distance travelled by the tip of the second hand of a clock in 1 minute if the hand is 6 cm long. Distance = cm

2) Arthur ran around a circular field 3 times. If he ran a total distance of 750 m, what is the diameter and radius of the field? diameter = m radius = m 3) Elena cycled to school. Find the distance travelled by Elena if her bicycle wheels rotated 840 times and the radius is 0.25 m. Distance = m

4) Charmaine has a circular garden that she separates into three equal parts. If the radius of the garden is 9 m, what is the length of the arc of each part? Length = m

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Area of a Circle (with detailed solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

2 October 2020

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Area of circles

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Circle worksheets: finding the area

Students determine the area of circles given the radius or the diameter .  Worksheets 1-3 are in customary units; 4-6 are metric. All worksheets are printable pdf files.

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Metric cm, m:

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More geometry worksheets

Browse all of our geometry worksheets , from the basic shapes through areas and perimeters, angles, grids and 3D shapes.

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Circle Theorems Practice Questions

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