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A closed cardboard box is to be designed for packing the

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Director
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A closed cardboard box is to be designed for packing the [#permalink] New post 13 Apr 2007, 10:14
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A closed cardboard box is to be designed for packing the cylindrical tube (figure attached). Will the entire tube fit inside the box?

(1) The empty box contains 3 cubic feet.

(2) The total surface area of the box is 14 square feet.

Please explain
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Manager
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 [#permalink] New post 14 Apr 2007, 01:39
We know the volume of the cylinder: 1/4*pie*4 = pie = 3.14

1. Empty box contain 3 cubic feet implies the volume is 3 < pie.
Therefore, cylinder won't fit , and A is sufficient

2. Total surface area is 14 implies 2xy + 2xz + 2yz = 14
but that's all we have so it's insufficient

Therefore, A.

Something to note perhaps: if the area of the cylinder were smaller than the area of the box, then still, we could not conclude that the cylinder would fit based on volume alone. Why? Because we're interested in putting the whole cylinder into the box, not the pieces of the cylinder. In that case, we would need to know more about the dimensions of the box. But this would make the problem very tricky so I am not surprised that in this question the cylinder has a smaller volume. This way, it automatically eliminates any possibilites of the box being large enough.
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 [#permalink] New post 14 Apr 2007, 07:26
What would be the minimum surface area needed?
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 [#permalink] New post 14 Apr 2007, 07:38
sorry I meant so say if the volume of the cylinder was smaller than the volume of the box .
  [#permalink] 14 Apr 2007, 07:38
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A closed cardboard box is to be designed for packing the

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