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Fun Guide to GCSE Circles: Area & Circumference Answers PDF

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Asna C

13/10/2022

Maths

Area and Circumference of Circles

Fun Guide to GCSE Circles: Area & Circumference Answers PDF

This GCSE area and circumference of circles study guide covers essential concepts and practice problems for calculating the area and circumference of circles. It provides step-by-step solutions and explanations for various circle-related questions.

Key points:

  • Introduces basic circle terminology and concepts
  • Covers formulas for area and circumference calculations
  • Includes practice problems with increasing complexity
  • Demonstrates problem-solving techniques for circle-related questions
  • Provides worked examples for GCSE-level circle problems
...

13/10/2022

901

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Circle Basics and Terminology

This page introduces fundamental concepts related to circles.

Question 1 asks students to draw and identify key parts of a circle:

  • Drawing a radius
  • Drawing and shading a sector

Question 2 tests students' knowledge of circle terminology:

  • Identifying a tangent alinethattouchesthecircleatasinglepointa line that touches the circle at a single point
  • Identifying a diameter alinesegmentthatpassesthroughthecenterofthecircleandhasitsendpointsonthecirclea line segment that passes through the center of the circle and has its endpoints on the circle

Definition: A radius is a line segment from the center of a circle to any point on its circumference.

Definition: A sector is a region of a circle enclosed by two radii and an arc.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Calculating Circumference and Area

This page focuses on applying formulas for circumference of a circle and area of a circle.

Question 3 involves calculating the circumference of a circle with a given radius:

  • Radius: 6.5 cm
  • Formula used: Circumference = 2πr
  • Answer required to 2 decimal places

Question 4 requires finding the area of a circle with a given diameter:

  • Diameter: 9 m
  • Formula used: Area = πr²
  • Answer required to 1 decimal place

Example: For Question 3, the calculation would be: Circumference = 2π6.56.5 ≈ 40.84 cm

Example: For Question 4, first calculate the radius 4.5m4.5 m, then: Area = π4.54.5² ≈ 63.6 m²

Questions 5 and 6 involve expressing answers in terms of π:

  • Question 5: Circumference of a circle with diameter 12 mm
  • Question 6: Area of a circle with radius 8 cm

Highlight: Expressing answers in terms of π often provides a more precise result than rounding to decimal places.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Advanced Circle Problems

This page presents more complex problems involving circles and semi-circles.

Question 7 is a multi-step problem involving a semi-circle:

  • Given the area of a semi-circle 50m250 m², students must find its perimeter
  • This requires working backwards from the area formula to find the radius, then calculating the circumference

Question 8 is a real-world application problem:

  • A circular field with a diameter of 32 meters
  • Students must calculate the cost of fencing the entire circumference at £15.95 per meter

Example: For Question 7, the steps would be:

  1. Use the semi-circle area formula: 50 = πr2πr²/2
  2. Solve for r: r ≈ 5.64 m
  3. Calculate the perimeter: πr + 2r ≈ 29.0 m

Highlight: These problems demonstrate how circle geometry concepts apply to real-world situations.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Compound Shapes with Circles

This page focuses on problems involving combinations of circles and other shapes.

Question 9 presents a compound shape consisting of a square and a semi-circle:

  • Students must calculate the total area and determine how many boxes of lawn seed are needed to cover it
  • This problem combines area calculations for different shapes and practical application

Question 10 involves finding the area of a ring theregionbetweentwoconcentriccirclesthe region between two concentric circles:

  • The ring is formed by cutting a smaller circle out of a larger one
  • Students must calculate and subtract the areas of both circles

Vocabulary: Concentric circles are circles that share the same center point but have different radii.

Example: For Question 10, the calculation would be: Area of ring = π7.57.5² - π66² ≈ 80.55 cm²

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Partial Circles and Sectors

This page deals with problems involving parts of circles and sectors.

Question 11 requires calculating the perimeter of three-quarters of a circle:

  • Radius given as 12 meters
  • Students must combine the circular arc length with two radii

Question 12 involves finding the area of a complex shape:

  • A semi-circle inside a quarter-circle sector
  • Students need to subtract the area of the semi-circle from the sector area

Definition: A sector is a part of a circle enclosed by two radii and an arc.

Highlight: These problems test students' ability to visualize and work with portions of circles, combining different formulas and concepts.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Circles and Squares

This page focuses on problems involving circles in relation to squares.

Question 13 presents a circle inscribed in a square:

  • The square has sides of 8 cm
  • Students must find the area of the shaded region theareabetweenthecircleandthesquarethe area between the circle and the square
  • This involves subtracting the area of the circle from the area of the square

Example: For Question 13, the steps would be:

  1. Calculate the square area: 8² = 64 cm²
  2. Calculate the circle area: π44² ≈ 50.3 cm²
  3. Subtract: 64 - 50.3 ≈ 13.7 cm²

Highlight: This type of problem tests students' ability to work with multiple shapes and use subtraction to find areas of irregular regions.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

View

Advanced Circle Relationships

The final page presents a complex problem involving the relationship between two circles.

Question 14 requires students to prove a relationship between a semi-circle and a smaller circle:

  • The semi-circle has a radius of 12 cm
  • Its area is 8 times the area of the smaller circle
  • Students must show that the radius of the smaller circle is 3 cm

This problem involves:

  • Using the area formulas for both shapes
  • Setting up an equation based on the given relationship
  • Solving the equation to find the radius of the smaller circle

Highlight: This question tests students' ability to work algebraically with circle formulas and demonstrate mathematical proof skills.

Example: The key steps in the solution are:

  1. Express the area of the semi-circle: 1/21/2π1212² = 72π
  2. Set up the equation: 72π = 8πr², where r is the radius of the smaller circle
  3. Solve to show that r = 3 cm

This final question serves as a challenging culmination of the concepts covered throughout the worksheet.

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Maths

901

13 Oct 2022

8 pages

Fun Guide to GCSE Circles: Area & Circumference Answers PDF

A

Asna C

@asnac_jhfz

This GCSE area and circumference of circles study guide covers essential concepts and practice problems for calculating the area and circumference of circles. It provides step-by-step solutions and explanations for various circle-related questions.

Key points:

  • Introduces basic circle terminology and... Show more

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Circle Basics and Terminology

This page introduces fundamental concepts related to circles.

Question 1 asks students to draw and identify key parts of a circle:

  • Drawing a radius
  • Drawing and shading a sector

Question 2 tests students' knowledge of circle terminology:

  • Identifying a tangent alinethattouchesthecircleatasinglepointa line that touches the circle at a single point
  • Identifying a diameter alinesegmentthatpassesthroughthecenterofthecircleandhasitsendpointsonthecirclea line segment that passes through the center of the circle and has its endpoints on the circle

Definition: A radius is a line segment from the center of a circle to any point on its circumference.

Definition: A sector is a region of a circle enclosed by two radii and an arc.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

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Improve your grades

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By signing up you accept Terms of Service and Privacy Policy

Calculating Circumference and Area

This page focuses on applying formulas for circumference of a circle and area of a circle.

Question 3 involves calculating the circumference of a circle with a given radius:

  • Radius: 6.5 cm
  • Formula used: Circumference = 2πr
  • Answer required to 2 decimal places

Question 4 requires finding the area of a circle with a given diameter:

  • Diameter: 9 m
  • Formula used: Area = πr²
  • Answer required to 1 decimal place

Example: For Question 3, the calculation would be: Circumference = 2π6.56.5 ≈ 40.84 cm

Example: For Question 4, first calculate the radius 4.5m4.5 m, then: Area = π4.54.5² ≈ 63.6 m²

Questions 5 and 6 involve expressing answers in terms of π:

  • Question 5: Circumference of a circle with diameter 12 mm
  • Question 6: Area of a circle with radius 8 cm

Highlight: Expressing answers in terms of π often provides a more precise result than rounding to decimal places.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Circle Problems

This page presents more complex problems involving circles and semi-circles.

Question 7 is a multi-step problem involving a semi-circle:

  • Given the area of a semi-circle 50m250 m², students must find its perimeter
  • This requires working backwards from the area formula to find the radius, then calculating the circumference

Question 8 is a real-world application problem:

  • A circular field with a diameter of 32 meters
  • Students must calculate the cost of fencing the entire circumference at £15.95 per meter

Example: For Question 7, the steps would be:

  1. Use the semi-circle area formula: 50 = πr2πr²/2
  2. Solve for r: r ≈ 5.64 m
  3. Calculate the perimeter: πr + 2r ≈ 29.0 m

Highlight: These problems demonstrate how circle geometry concepts apply to real-world situations.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Compound Shapes with Circles

This page focuses on problems involving combinations of circles and other shapes.

Question 9 presents a compound shape consisting of a square and a semi-circle:

  • Students must calculate the total area and determine how many boxes of lawn seed are needed to cover it
  • This problem combines area calculations for different shapes and practical application

Question 10 involves finding the area of a ring theregionbetweentwoconcentriccirclesthe region between two concentric circles:

  • The ring is formed by cutting a smaller circle out of a larger one
  • Students must calculate and subtract the areas of both circles

Vocabulary: Concentric circles are circles that share the same center point but have different radii.

Example: For Question 10, the calculation would be: Area of ring = π7.57.5² - π66² ≈ 80.55 cm²

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Partial Circles and Sectors

This page deals with problems involving parts of circles and sectors.

Question 11 requires calculating the perimeter of three-quarters of a circle:

  • Radius given as 12 meters
  • Students must combine the circular arc length with two radii

Question 12 involves finding the area of a complex shape:

  • A semi-circle inside a quarter-circle sector
  • Students need to subtract the area of the semi-circle from the sector area

Definition: A sector is a part of a circle enclosed by two radii and an arc.

Highlight: These problems test students' ability to visualize and work with portions of circles, combining different formulas and concepts.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Circles and Squares

This page focuses on problems involving circles in relation to squares.

Question 13 presents a circle inscribed in a square:

  • The square has sides of 8 cm
  • Students must find the area of the shaded region theareabetweenthecircleandthesquarethe area between the circle and the square
  • This involves subtracting the area of the circle from the area of the square

Example: For Question 13, the steps would be:

  1. Calculate the square area: 8² = 64 cm²
  2. Calculate the circle area: π44² ≈ 50.3 cm²
  3. Subtract: 64 - 50.3 ≈ 13.7 cm²

Highlight: This type of problem tests students' ability to work with multiple shapes and use subtraction to find areas of irregular regions.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Circle Relationships

The final page presents a complex problem involving the relationship between two circles.

Question 14 requires students to prove a relationship between a semi-circle and a smaller circle:

  • The semi-circle has a radius of 12 cm
  • Its area is 8 times the area of the smaller circle
  • Students must show that the radius of the smaller circle is 3 cm

This problem involves:

  • Using the area formulas for both shapes
  • Setting up an equation based on the given relationship
  • Solving the equation to find the radius of the smaller circle

Highlight: This question tests students' ability to work algebraically with circle formulas and demonstrate mathematical proof skills.

Example: The key steps in the solution are:

  1. Express the area of the semi-circle: 1/21/2π1212² = 72π
  2. Set up the equation: 72π = 8πr², where r is the radius of the smaller circle
  3. Solve to show that r = 3 cm

This final question serves as a challenging culmination of the concepts covered throughout the worksheet.

Name:
Instructions
●
Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
●
Area and Circu

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Area and Circumference of Circles Worksheet

This GCSE 191-9 mathematics worksheet focuses on the area and circumference of circles. It contains 14 questions of varying difficulty, designed to test and reinforce students' understanding of circular geometry.

Highlight: The worksheet covers a range of topics from basic circle terminology to complex problem-solving involving circular shapes.

Key features of the worksheet include:

  • Clear instructions for students
  • A variety of question types, from simple definitions to multi-step problems
  • Emphasis on showing all working out
  • Questions that integrate real-world applications

Vocabulary: GCSE GeneralCertificateofSecondaryEducationGeneral Certificate of Secondary Education is the main school-leaving qualification in England, Wales, and Northern Ireland.

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Paul T

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user