29
ܵ ௬ௗ ൌ ߨ ൈ ݎ ଷ ܵ ൌ 1 3 ൈ ݎߨ ଷ ቑ ֜ ܵ ு௦ ൌ 2 3 ൈ ߨ ൈ ݎ ଷ
3.3.3 Complete Sphere Respecting the previous steps, the volume of a sphere would be :
ܵ ௌ ൌ 2 ൈ ܵ ு௦ ܵ ௌ ൌ 2 ൈ 2 3 ൈ ߨ ൈ ݎ ଷ ܵ ௌ ൌ 4 3 ൈ ߨ ൈ ݎ ଷ
4 Further steps What other volumes can be found by propagating Cavalieri’s Principle? Is it possible to use this principle to work out the volume of a doughnut? Furthermore, this technique might help you to solve the “The napkin ring problem” and find the volumes of Cycloids.
5 Reference Zill, D. (2009) Calculus: Early Transcendentals, Jones Bartlett Learning.
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Division by 7
Multiply the last digit by 2. Subtract this answer from the remaining digits. Is this number evenly divisible by 7? If it is, then your original number is evenly divisible by 7. Try 364. 4, the last digit, multiplied by 2 = 8. 36, the remaining digits, minus 8 = 28. The last time I checked, 28 is evenly divisible by 7, and thus, so is 364!
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