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The inside dimensions of a rectangular wooden box are 4 mete

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

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New post 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?

(A) \(20 \pi\)

(B) \(24 \pi\)

(C) \(25 \pi\)

(D) \(96 \pi\)

(E) \(100 \pi\)
[Reveal] Spoiler: OA

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

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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.

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

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New post 09 Mar 2013, 01:59
megafan wrote:
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?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8


Discussed here: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.html

Similar question to practice: a-rectangular-box-has-dimensions-12-10-8-inches-what-is-the-28790.html

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

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

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New post 17 Feb 2015, 20:05
I am a bid confused by this question.. so does the base of the cylinder have to be a circle and cannot be an oval shape?

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

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New post 17 Feb 2015, 21:12
Hi scholar1,

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.

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

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Hello from the GMAT Club BumpBot!

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

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New post 09 Sep 2017, 13:44
although there is a word "upright", the height and other dimensions of the box still vary in different situations.

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Re: The inside dimensions of a rectangular wooden box are 4 mete   [#permalink] 09 Sep 2017, 13:44
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