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The Circle

Learn the main parts of a circle, including radius, diameter, and circumference. Discover how to find the diameter using the circumference formula and calculate the area of a circle. Practice exercises provided.

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The Circle

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  1. The Circle Circumference of the circle Diameter = Circumference ÷π www.mathsrevision.com Area of a circle Fractions of a circle Created by Mr. Lafferty Maths Dept.

  2. Starter Questions 3cm www.mathsrevision.com 6cm Created by Mr. Lafferty Maths Dept.

  3. Main Parts of a Circle Revision of 2 Learning Intention Success Criteria • To revise the basics of the circle. • 1. Remember the terms circumference, diameter and radius. • 2. Identify them on a circle. • 3. Calculate the circumference using formula. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. radius Diameter Circumference Main Parts of a Circle Revision of 2 Main parts of the circle O www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  5. Main part of a Circle Revision of 2 Example : Find the length of the circumference (Perimeter) of each circle 2cm 10cm www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  6. Main part of a Circle Revision of 2 Now try Exercise 1 Ch29 (page 118) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  7. Starter Questions 8 5 4 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  8. Finding the Diameter The Circle Learning Intention Success Criteria • Understand how to rearrange circumference formula to find diameter. • 1. We are learning we can find diameter of a circle if we know the circumference. • 2. Solve diameter problems. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  9. Finding the Diameter The Circle We can easily rearrange the circumference formula so that we have the diameter D on one side. You have 1 minute to rearrange equation. www.mathsrevision.com Remember change side change sign Created by Mr. Lafferty Maths Dept.

  10. Finding the Diameter The Circle Example : Find the diameter of each circle given the circumference. C = 62.8 cm C =15.7 cm 5cm 20cm www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  11. Finding the Diameter The Circle Now try Exercise 2 Ch29 (page 121) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  12. Starter Questions 6 5 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  13. Peeling an orange Area of a Circle A circumference A B x x O O www.mathsrevision.com • What do we call the distance OA in terms of • the large circle. • What do we call the distance AB in terms of the large circle.

  14. A B x O Area of a Circle • What is the formula for the area • of a right-angle triangle. • Use this formula to work out • the area for a circle. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  15. If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. 1 8 2 2 7 1 3 6 5 8 6 4 4 3 7 5 Area of a Circle www.mathsrevision.com Demo Created by Mr Lafferty

  16. If we cut the sectors Thinner and thinner then we get closer and closer to a rectangle. Hence we can represent the area of a circle by a rectangle. 8 6 4 2 3 7 1 5 thinner and thinner sectors Area of a Circle www.mathsrevision.com Created by Mr Lafferty

  17. Area of a Circle www.mathsrevision.com But the area inside this rectangle is also the area of the circle Area = πr2 Created by Mr Lafferty

  18. Area of a circle Solution Q.Find the area of the circle ? 4cm www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  19. Area of a circle Solution • The diameter of the circle is 60cm. • Find area of the circle? www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  20. Area of a Circle What have we learned so far www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  21. Area of a Circle Now try Exercise 3 Ch29 (page 123) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  22. Starter Questions 4 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  23. Mixed Problems The Circle Learning Intention Success Criteria • Recall knowledge of circles so far. • 1. We are learning to solve problems by applying our knowledge of circles. • 2. Solve mixed problems by applying all our knowledge so far. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  24. Mixed Problems The Circle Things to think about when doing exercise. The area of a semicircle ……. Find whole circle then half it ! The area of a quarter circle …….Find whole circle then quarter it ! www.mathsrevision.com Composite area …….Find each area and add them together ! Created by Mr. Lafferty Maths Dept.

  25. 5 cm 20cm Mixed Problems The Circle Example 1 : Find the area of the shape Area = rectangle + semicircle www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  26. Mixed Problems The Circle Example 2 : A circle is contained in a square. Find the grey shaded area below. Area = square - circle 8cm www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  27. Mixed Problems The Circle Now try Exercise 4 Ch29 (page 125) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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