Cookie Size Comparison Based on Average Radius

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Comparing two pairs of cookies with average radii of 8 cm and 7 cm respectively. Through a series of adjustments to maintain an average radius of 7 cm, the total area, individual areas, and target average area per cookie are calculated for various cookie size combinations. The analysis aims to find the optimal cookie size combination based on area considerations.


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  1. Two Pairs of Cookies One with average radius of 8 cm Other with average radius of 7 cm Which pair of cookies would you prefer?

  2. 8-cm Cookie

  3. 2 Cookies Total cookie area = 2 82 = 2 (64) Area of average Cookie = 64 8-cm Cookie

  4. 7-cm Cookie

  5. 2 Cookies Total cookie area = 2 72 = 2 (49) Area of average Cookie = 49 7-cm Cookie We are now going to start making two unequal size cookies, one smaller and one larger, always keeping the average radius of the two cookies equal to 7 cm, the initial radii of the two cookies. Each time we will compute the total area of the two cookies and the average area per cookie..

  6. 8-cm Cookie 6-cm Cookie

  7. Total cookie area = 82 + 62 = 100 = 2 (50) TARGET: Making Area of average cookie > 64 Area of average cookie = (50) 8-cm Cookie 6-cm Cookie

  8. 9-cm Cookie 5-cm Cookie

  9. Total cookie area = 92 + 52 = 106 = 2 (53) TARGET: > 64 Area of average cookie = (53) 9-cm Cookie 5-cm Cookie

  10. 10-cm Cookie 4-cm Cookie

  11. Total cookie area = 102 + 42 = 116 = 2 (58) TARGET: > 64 Area of average cookie = (58) 10-cm Cookie 4-cm Cookie

  12. 11-cm Cookie 3-cm Cookie

  13. Total cookie area = 112 + 32 = 130 = 2 (65) TARGET: > 64 Area of average cookie = (65) 11-cm Cookie 3-cm Cookie

  14. 12-cm Cookie 2-cm Cookie

  15. Total cookie area = 122 + 22 = 148 =2 (74) TARGET: > 64 Area of average cookie = (74) 12-cm Cookie 2-cm Cookie

  16. 13-cm Cookie 1- cm

  17. Total cookie area = 132 + 12 = 170 =2 (85) TARGET: > 64 Area of average cookie = (85) 13-cm Cookie 1- cm

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