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Christmas Tree Volume

Christmas Tree Volume. 17 Sections 181 Data Points Disk and Washer Method used to find volume. Section 1 – Method: Washer Integral: p [ 3.8 0.35 (.235x 3 – 2.74x 2 + 9.626x + 7.488) 2 – (.1716x 4 – 1.6199x 3 + 5.5448x 2 – 10.4472x + 13.2523) 2 dx Volume: 17101.80 mm 3.

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Christmas Tree Volume

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  1. Christmas Tree Volume

  2. 17 Sections • 181 Data Points • Disk and Washer Method used to find volume

  3. Section 1 – Method: Washer Integral: p[3.80.35 (.235x3 – 2.74x2 + 9.626x + 7.488)2 – (.1716x4 – 1.6199x3 + 5.5448x2 – 10.4472x + 13.2523)2dx Volume: 17101.80 mm3

  4. Section 2 – Method: Disk Integral: p[53.8 (-1.53x3 + 20.95x2 – 96.567x + 164.82)2dx Volume: 5724.36 mm3

  5. Section 3 – Method: Disk Integral: p[7.65 (.4143x3 – 8.7318x2 + 60.4227x – 122.5632)2dx Volume: 11362.96 mm3

  6. Section 4 – Method: Disk Integral: p[11.97.6 (-.06458x4 + 2.6434x3 – 40.465x2 + 273.5502x – 672.386)2dx Volume: 17885.15 mm3

  7. Section 5 – Method: Washer Integral: p[12.211.9 (-2.5x2 + 59.25x – 338.95)2 – (x – 11.5)2dx Volume: 879.7652 mm3

  8. Section 6 – Method: Washer Integral: p[12.712.2 (-1.4896x2 + 39.0832x – 243.2927)2 – (x – 11.5)2dx Volume: 1560.28 mm3

  9. Section 7 – Method: Washer Integral: p[14.812.7 (.5384x3 – 22.4604x2 + 310.8937x – 1415.9257)2 – (1)2dx Volume: 6159.14 mm3

  10. Section 8 – Method: Washer Integral: p[19.514.8 (.04731x4 – 3.09185x3 + 74.948x2 -798.3365x +3163.4085)2 – (1)2dx Volume: 12184.44 mm3

  11. Section 9 – Method: Washer Integral: p[21.819.5 (1.1474x3 – 72.0222x2 + 1504.7228x – 10454.412)2 – (1)2dx Volume: 4230.77 mm3

  12. Section 10 – Method: Washer Integral: p[25.721.8 (.3329x3 – 24.2315x2 + 586.1303x – 4703.2505)2 – (1)2dx Volume: 5303.72 mm3

  13. Section 11 – Method: Washer Integral: p[26.525.7 (4.1667x3 – 326.9643x2 + 8553.4048x – 74588.1)2 – (1)2dx Volume: 699.00 mm3

  14. Section 12 – Method: Washer Integral: p[27.4526.5 (.5469x3 – 45.1543x2 + 1241.2663x – 11354.36)2 – (27.5 – x)2dx Volume: 932.03 mm3

  15. Section 13 – Method: Disk Integral: p[28.2527.45 (2.22x3 – 18.50975x2 + 5143.0062x – 47615.3198)2dx Volume: 598.94 mm3

  16. Section 14 – Method: Disk Integral: p[31.6528.25 (.2156x3 – 19.8274x2 + 606.7192x – 6171.9353)2dx Volume: 2342.68 mm3

  17. Section 15 – Method: Disk Integral: p[34.331.65 (.4887x3 – 49.2722x2 + 1654.781x – 18507.6127)2dx Volume: 1174.96 mm3

  18. Section 16 – Method: Disk Integral: p[37.234.3 (.3307x3 – 36.1048x2 + 1312.715x – 15890.971)2dx Volume: 908.16 mm3

  19. Section 17 – Method: Disk Integral: p[40.137.2 (.3903x3 – 45.9024x2 + 1798.2987x – 23464.8916)2dx Volume: 667.86 mm3

  20. Total Volume: 89715.01 mm3

  21. What Could Be More Fun Than Facts? • In 1510 the first known decorated Christmas tree appeared in Riga, Latvia • One acre of Christmas trees produces the daily oxygen requirement for 18 people. • Approximately 30 million real Christmas trees are sold in North America every year, totally over $1.2 billion in sales.  About 78% of these are pre-cut trees and 22% cut-your-own. • Only seven months, four days, 15 hours, and 23 minutes (at the beginning of this period) until CHRISTMAS

  22. Don’t be naughty…

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