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megafan
Joined: 28 May 2009
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Schools: Stern PT Fall'18 Booth PT '18
GMAT Date: 03-22-2013
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08 Mar 2013, 11:41
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (02:19) correct
43%
(02:26)
wrong
based on 174
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Not Attempted Yet
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) \(100 \pi\)
(A) \(20 \pi\)
(B) \(24 \pi\)
(C) \(25 \pi\)
(D) \(96 \pi\)
(E) \(100 \pi\)
harsh6239
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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.
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.
General Discussion
09 Mar 2013, 01:59
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megafan
"Stolen" question from GMAT Prep:
Quote:
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.
