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Understanding the Area and Circumference of Circles: A Comprehensive Guide

This guide explores the principles of finding the area and circumference of circles, utilizing the formula A = πr². It includes practical exercises, allowing you to practice calculating the area of various circles and shaded regions. Additionally, learn how to derive the radius and circumference from given areas. Examples include calculating areas based on diameters and square dimensions. Master these concepts to enhance your understanding of circles in geometry.

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Understanding the Area and Circumference of Circles: A Comprehensive Guide

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  1. Area of Circles and Parts of Circles

  2. Finding the area of a circle The area of a circle is found using the formula A = r2

  3. Practice Finding the area of a circle A = r2 A = (2.17)2 A = 4.7089 cm2 or 14.79 cm2

  4. Practice Finding the area of a circle A = r2 A = (5.19/2)2 A = 6.734 cm2 or 21.16 cm2

  5. Practice Finding the area of a circle Find the area of the shaded region A = 36 - 9 = 27 u2 or 84.82 u2 3 6

  6. Practice Finding the area of a circle Find the area of the circle if the area of the square = 144 m2 The circle has a diameter of 12 m so A = 36 m2 or 113.1 m2

  7. Practice Finding the area of a circle Find the area of the shaded region if the side of the square = 10 cm The area is 100 cm2 - 25 cm2 or 21.46cm2

  8. Practice Finding the area of a circle Find the area of the shaded region if the side of the square is 12 cm. The area is 144 cm2 - 4(9) cm2 or 30.9 cm2

  9. Finding the radius when area is known Since the formula for the area of a circle is A = πr2, the radius can be determined if the area is known. If A = 49π, then r2 = 49. If r2 = 49, then r = 7.

  10. Finding the radius when area is known Find the radius for each circle • A = 144π • A = 36π • A = 81π • A = 25π 5. A = 100π r = 12 r = 6 r = 9 r = 5 r = 10

  11. Finding the circumference when area is known To find the circumference when the area is known, first find the radius and then use it to find the circumference. A = 49π so r = 7 and d = 14 C = 14π

  12. Finding the circumference when area is known Find the circumference for each circle • A = 144π • A = 36π • A = 81π • A = 25π 5. A = 100π C = 24π C = 12π C = 18π C = 10π C = 20π

  13. THE END

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