Give a quick stream of consciousness before answering the following question. 189. The inside dimensions of a rectangular wooden box\nare 10 inches by 12 inches by 14 inches. A cylindrical\ncanister is to be placed inside the box so that it stands\nupright when the closed box rests on one of its six\nfaces. Of all such canisters that could be used, what is\nthe radius, in inches, of the one that has maximum\nvolume?\nOptions:\n(A)  3\n(B)  4\n(C)  5\n(D)  6\n(E)  8
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Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 14x12 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 12, so the radius will be 6.
The answer: (D).
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