Bunuel wrote:

Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?

A. 48π

B. 27π

C. 12π

D. 9π

E. 6.75π

As we're asked for the maximal possible value, we'll look at the extremes.

This is a Logical approach.

We are told that width = 3, length = 12 and height = 4.

Then the diameter of the circle is at most 3 and the height at most 4.

This gives a total volume of (1.5)^2 * 4 * pi = 9pi per cylinder.

(D) is our answer.

Instead of figuring out all the different arrangements, we'll first try estimating.

This is an Alternative approach.

Note that we could also have guessed that this is the answer rather easily (an Alternative approach):

Dividing the box into 4 equal parts of 3*3*4 gives a total volume of 36 for the box enclosing the cylinder.

Since (A), (B), (C) are all larger than this, they are eliminated.

Even without calculating, we can eyeball that (E) looks way too small and so (D) is a much better bet.

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