作者SDUM (Roger)
看板trans_math
标题Re: [积分] 积分应用
时间Sat Mar 21 11:48:24 2009
※ 引述《gerry99921 (damnu)》之铭言：
: A wedge is cut out of a circular cylinder of radius 6 by two planes.
: One plane is perpendicular to the axis of the cylinder,
: the other intersects the first at an angle of 30 degrees
: along a diameter of the cylinder.
: Find the volume of the wedge.
: 这是题目 请高手帮忙解题谢谢
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1.将他分成无限多个三角柱
假设该三角柱距离圆心x，厚度 dx
√(36-x^2)
dV= 0.5．√(36-x^2)．────── dx
√3
6 √(36-x^2)
V=∫dV = ∫ 0.5．√(36-x^2)．────── dx = 48√3
-6 √3
2.将他分成无限多个长方柱
假设该长方柱距离直径x，厚度 dx
x
dV= 2√(36-x^2)．─── dx
√3
6 x
V=∫dV = ∫ 2√(36-x^2)．─── dx = 48√3
0 √3
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