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The inside dimensions of a rectangular wooden box are 4 mete [#permalink]

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08 Mar 2013, 11:41

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The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum 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 drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?

Re: The inside dimensions of a rectangular wooden box are 4 mete [#permalink]

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08 Mar 2013, 12:17

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You have three options here. My approach is to calculate volumes for all of them and see which one is greatest.

1. Cylinder's base rests on a 4x5 side of the box. So, height becomes 6 and the maximum possible radius becomes 4/2.

So, maximum volume = \(\pi . (4/2)^2 . 6 = \pi 24\)

2. Cylinder's base rests on a 5x6 side of the box. So, height becomes 4 and the maximum possible radius becomes 5/2.

So, maximum volume = \(\pi . (5/2)^2 . 4= \pi 25\)

3. Cylinder's base rests on a 4x6 side of the box. So, height becomes 5 and the maximum possible radius becomes 4/2.

So, maximum volume = \(\pi . (4/2)^2 . 5 = \pi 20\)

Option 2 gives maximum value and so that should be the answer,\(\pi 25.\)

In hindsight you can see that since in volume of a cylinder \((\pi r^2 h)\) the radius r has a higher power, the one with a higher radius will have maximum volume when other parameters are close to each other (like 4,5 and 6). You get maximum radius when base is kept on a 6x5 face. Still, personally I will go with finding all three volumes and then comparing them.

The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum 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 drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?

(A) \(20 \pi\)

(B) \(24 \pi\)

(C) \(25 \pi\)

(D) \(96 \pi\)

(E) \(100 \pi\)

"Stolen" question from GMAT Prep:

Quote:

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 canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

Re: The inside dimensions of a rectangular wooden box are 4 mete [#permalink]

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17 Feb 2015, 19:40

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By definition, a cylinder has a base that is a circle; this impacts a variety of questions that can be asked about a cylinder (volume, surface area, width, etc.). In this question, the width of the cylinder (re: the diameter) will be influenced by how it is "oriented" inside the box (for that matter, so will the height). Depending on which side is the "base" of the box, the maximum possible diameter of the cylinder (and the maximum height of the cylinder) will change.

Re: The inside dimensions of a rectangular wooden box are 4 mete [#permalink]

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08 Oct 2016, 06:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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