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# the inside dimensions of a rectangular wooden box are 6

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Director
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the inside dimensions of a rectangular wooden box are 6 [#permalink]  15 Mar 2007, 09:04
the inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. a cylindrical canister 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 cansiters that could be used, what is the radius, in inches, of the one that has max volume?

3
4
5
6
8

the answer is NOT c. can anyone explain why? I've attached an overhead representation of the canister inscribed within the wooden box. assume the height of the box is 8 and the length and width are 10 and 6 respectively. why can't we use V=(pi)(5^2)(8) to calc. the max volume
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WOODEN_DIAGRAM.doc [50.5 KiB]

Director
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[#permalink]  15 Mar 2007, 09:30
Because it wont fit

assume that two sides are of 8 and 10inches, then to fit the cylinder it should have diameter of 8 and not 10, as one side is only 8, which is lesser than the assumed diameter of 10.

For any two sides diameter of the bottom of the cylinder will be the shorter side.

Isnt the answer is 4.

regards,

Amardeep
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[#permalink]  15 Mar 2007, 09:37
The biggest volume is when the radius is going to be the largest Im guessing, because that is squared and will contribute the most to the volume.

So using your diagram, consider the 2 best possibilities:

1. The height is 8 and the width is 10, thus the length (the dimension you didn't show) is 6.

If this is the case, the radius has to be at max 8/2=4. If it were 5 it wouldnt fit inside the box.

So the volume is 6*pi*16

2. The height is 6 and the width is 10, thus the length is 8

So the volume is 8*pi*9

So #1 gives the greatest volume, therefore I would say B, 4 is the radius.
[#permalink] 15 Mar 2007, 09:37
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# the inside dimensions of a rectangular wooden box are 6

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