Difficult Question
2010-02-14 2:50 am
John has a circular piece of paper with radius a, he cuts it to the form of a sector and then fold it to make a paper cone with maximum volume, at what angle that John has cut the piece of paper ?
回答 (2)
2010-02-14 5:47 pm
✔ 最佳答案
Using Lagrange Multiplier, the question can be simplified.2010-02-14 09:34:42 補充：
this even don't required lagrange multiplier, it is simply a differentiation question.
2010-02-14 09:47:09 補充：
Please look at the following answer:
圖片參考：http://i726.photobucket.com/albums/ww265/physicsworld2010/ScreenHunter_01Feb140945.jpg?t=1266111995
http://i726.photobucket.com/albums/ww265/physicsworld2010/ScreenHunter_01Feb140945.jpg?t=1266111995
參考: Physics king
2010-02-14 5:52 am
This question is very complicated.
Let θ be the angle that can obtain the max. volume
we have,
arc length = θ/360 *2pi a
base circumference of the cone = θ/360 * 2pi a
Let r be the radius of the base circumference
2 pi r = θ/360 *2pi a
r = aθ/360
Height of the cone = √[a^2 - (a^2 θ^2/360^2)]
Let θ be the angle that can obtain the max. volume
we have,
arc length = θ/360 *2pi a
base circumference of the cone = θ/360 * 2pi a
Let r be the radius of the base circumference
2 pi r = θ/360 *2pi a
r = aθ/360
Height of the cone = √[a^2 - (a^2 θ^2/360^2)]
收錄日期: 2021-04-19 21:23:27
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