问题
单项选择题
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of the one that has maximum volume ？（）
A．3
B．4
C．5
D．6
E．8
答案
参考答案：B
解析：
根据题意可知，该圆柱体罐子一定内切于该长方体盒子，圆柱体底面的直径与高直接与该长方体盒子以哪一个面为底有关，长方体有三个不同的底面，所以此题可以分三种情况进行讨论：
圆柱体的体积为：πr2·h
(1)当圆柱体的底面与长方体的6 inches by 8 inches面重合时，其体积=90π
(2)当圆柱体的底面与长方体的8 inches by 10 inches面重合时，其体积=96π
(3)当圆柱体的底面与长方体的6 inches by 10 inches面重合时，其体积=72π
根据以上分析可知，该圆柱体的体积最大时其半径为4时。