求NN们解一道prep exam3（楼主自己又买的……）的数学题

wxdinefforts · 发表于 2014-8-12 15:32:53

The measurements obtained for the interior dimensions of a rectangular box are 200 centimeters by 200 centimers by 300 centimeters. If each of the three measurments has an error of at most 1 centimeter, which of the following is closet to the maxium possible difference, in cubic centimerters, betwwen the actual capacity of the box and the capacity computed using these measurements?
答案是160000
各位NN 这个怎么解啊

neacholas · 发表于 2014-8-12 15:48:49

301*201*201 - 300*200*200

反调戏 · 发表于 2014-8-12 17:58:36

自己又买的啥意思？

waq941111 · 发表于 2014-8-12 18:18:11

楼主的意思是有没有简单的算法啊？而且301*201*201-300*200*200和300*200*200-299*199*199比也不知道哪个差值更大啊？总不至于都算一遍吧。

wxdinefforts · 发表于 2014-8-13 07:43:51

对啊对啊

HermanLu · 发表于 2014-8-13 10:14:13

误差1 说明上下可以浮动0.5
于是
（300+0.5）*（200+0.5）*（200+0.5）-（300-0.5）*（200-0.5）*（200-0.5）
=（300*200*200+0.5*200*200+0.5*200*200+0.5*200*300+0.5*0.5*0.5）-（300*200*200-0.5*200*200-0.5*200*200-0.5*200*300-0.5*0.5*0.5）[去掉0.125这样极小的]
=0.5*100*100[（2*2+2*3+2*3）+（2*2+2*3+2*3）]
=160000

Zachary.ZX · 发表于 2019-12-12 20:33:38

我实在想知道简便方法就从Google上搜了

Let L = 200, W = 200, and H = 300.
When each dimension changes by 1cm, the result is the following:

The LENGTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- W*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The WIDTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The HEIGHT changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*W -- will change by 1cm:
1 * 200 * 200 = 40000.

Note:
Because each dimension is included in 2 of the 3 products above, there is some OVERLAP among the 3 changes in volume.
Thus:
Approximate total change in volume = 60000 + 60000 + 40000 = 160000.

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求NN们解一道prep exam3（楼主自己又买的……）的数学题

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