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Finding Radius and Diameter of Circles through Area and Circumference Calculations

This instructional guide demonstrates how to determine the radius and diameter of circles using trial and error methods based on their area and circumference. In the first example, we calculate the radius of a circle with an area of 78.5 cm² by testing various radius values until we find the correct one. The second example explores finding the radius from a given circumference of 20 cm. Utilizing the formulas for area (A = πr²) and circumference (C = 2πr), we clarify the process of achieving accurate results.

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Finding Radius and Diameter of Circles through Area and Circumference Calculations

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  1. Determining Radius and Diameter

  2. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Determining Radius and Diameter

  3. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Determining Radius and Diameter

  4. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → Determining Radius and Diameter

  5. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 Determining Radius and Diameter

  6. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm Determining Radius and Diameter

  7. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Determining Radius and Diameter

  8. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Determining Radius and Diameter

  9. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Try r = 5 cm → Determining Radius and Diameter

  10. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Try r = 5 cm → A = π r2 Determining Radius and Diameter

  11. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Try r = 5 cm → A = π r2 = 3.14 x 5 cm x 5 cm Determining Radius and Diameter

  12. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Try r = 5 cm → A = π r2 = 3.14 x 5 cm x 5 cm = 78.5 cm2 Determining Radius and Diameter

  13. Ex 1) Find the radius of a circle with an area of 78.5 cm2. Solve by Trial and Error: Try r = 3 cm → A = π r2 = 3.14 x 3 cm x 3 cm = 28.26 cm2 Too low. Try r = 5 cm → A = π r2 = 3.14 x 5 cm x 5 cm = 78.5 cm2 That’s it. Determining Radius and Diameter

  14. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Determining Radius and Diameter

  15. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Determining Radius and Diameter

  16. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → Determining Radius and Diameter

  17. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr Determining Radius and Diameter

  18. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Determining Radius and Diameter

  19. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Determining Radius and Diameter

  20. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → Determining Radius and Diameter

  21. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → C = 2πr Determining Radius and Diameter

  22. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → C = 2πr = 2 x 3.14 x 4 cm = 25.12 cm Determining Radius and Diameter

  23. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → C = 2πr = 2 x 3.14 x 4 cm = 25.12 cm Too high. Determining Radius and Diameter

  24. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → C = 2πr = 2 x 3.14 x 4 cm = 25.12 cm Too high. But which is closer? Determining Radius and Diameter

  25. Ex 2) Find the radius, to the nearest cm, of a circle with a circumference of 20 cm. Solve by trial and error: Try r = 3 cm → C = 2πr = 2 x 3.14 x 3 cm = 18.84 cm Too low. Try r = 4 cm → C = 2πr = 2 x 3.14 x 4 cm = 25.12 cm Too high. But which is closer? 18.84 cm is closer to 20 cm, so the radius is approximately 3 cm. Determining Radius and Diameter

  26. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. Determining Radius and Diameter

  27. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. Solve by working backwards through the formula: Determining Radius and Diameter

  28. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. Solve by working backwards through the formula: We know that to go from radius to area, we must; Determining Radius and Diameter

  29. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. Solve by working backwards through the formula: We know that to go from radius to area, we must; - square the radius Determining Radius and Diameter

  30. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • - multiply by 3.14 Determining Radius and Diameter

  31. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • - multiply by 3.14 (A = πr2) Determining Radius and Diameter

  32. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • multiply by 3.14 (A = πr2) • So, to go from area to radius, we must do the opposite; Determining Radius and Diameter

  33. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • multiply by 3.14 (A = πr2) • So, to go from area to radius, we must do the opposite; • - divide by 3.14 Determining Radius and Diameter

  34. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • multiply by 3.14 (A = πr2) • So, to go from area to radius, we must do the opposite; • divide by 3.14 • - find the square root of r2 Determining Radius and Diameter

  35. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. • Solve by working backwards through the formula: • We know that to go from radius to area, we must; • square the radius • multiply by 3.14 (A = πr2) • So, to go from area to radius, we must do the opposite; • divide by 3.14 • - find the square root of r2 (r = √A / π) Determining Radius and Diameter

  36. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. r = √A / π Determining Radius and Diameter

  37. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. r = √A / π = √145.19 cm2 / 3.14 Determining Radius and Diameter

  38. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. r = √A / π = √145.19 cm2 / 3.14 = √46.23885. . . cm2 Determining Radius and Diameter

  39. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. r = √A / π = √145.19 cm2 / 3.14 = √46.23885. . . cm2 ≈ 6.8 cm Determining Radius and Diameter

  40. Ex 3) Determine the radius, to the nearest tenth of a centimetre, of a circle with an area of 145.19 cm2. r = √A / π = √145.19 cm2 / 3.14 = √46.23885. . . cm2 ≈ 6.8 cm The radius of the circle is 6.8 cm, rounded to the nearest tenth. Determining Radius and Diameter

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