It is currently 12 Dec 2017, 19:43

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A solid cube is placed in a cylindrical container. Which of the follow

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 29 Aug 2010
Posts: 15

Kudos [?]: 15 [0], given: 124

A solid cube is placed in a cylindrical container. Which of the follow [#permalink]

Show Tags

New post 29 Oct 2017, 21:47
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (01:41) correct 49% (02:19) wrong based on 41 sessions

HideShow timer Statistics

A solid cube is placed in a cylindrical container. Which of the following percent values COULD possibly represent the ratio of the volume of the cylinder not occupied by the cube to the volume of the cylinder? (Assume the value of \(\pi\) to be 3)

(A) 16%
(B) 25%
(C) 28%
(D) 32%
(E) 36%
[Reveal] Spoiler: OA

Kudos [?]: 15 [0], given: 124

Manager
Manager
User avatar
S
Joined: 05 Dec 2016
Posts: 248

Kudos [?]: 26 [0], given: 49

Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
GMAT ToolKit User
Re: A solid cube is placed in a cylindrical container. Which of the follow [#permalink]

Show Tags

New post 29 Oct 2017, 23:37
Let's consider extreme situation:
Assume that cube is inscribed into the cylinder, then the ratio of its sides to radius of cylinder would be 2^1/2 to 1.
Volume of cube=(2^1/2)^3=2^3/2=2*2^1/2
Volume of cylinder=3*1^2*2^1/2=3*2^1/2
Volume of space in cylinder not occupied by cube=3*2^1/2-2*2^1/2=2^1/2
Ratio of volume not occupied by cube to volume of cylinder= 2^1/2 : 3*2^1/2=1/3

(a) 16%
Means that remaining 84% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(b) 25%
Means that remaining 75% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(c) 28%
Means that remaining 72% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(d) 32%
Means that remaining 68% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(e) 36%
Means that remaining 64% is occupied by cube, which CAN be true because maximum possible occupied space for cube would be 66,66%
Hence we can infer that cube is not inscribed in the cylinder.

Answer E.

Kudos [?]: 26 [0], given: 49

1 KUDOS received
Intern
Intern
avatar
B
Joined: 29 Aug 2010
Posts: 15

Kudos [?]: 15 [1], given: 124

Re: A solid cube is placed in a cylindrical container. Which of the follow [#permalink]

Show Tags

New post 30 Oct 2017, 22:25
1
This post received
KUDOS
Let us consider the situation where the largest possible cube (shaded in grey) fits perfectly in a particular cylinder as shown in the diagram below; however, the question does not state that we must fit in a largest possible cube into the cylinder.

Let the edge of the cube be \(a\).
Since the cube has to have a perfect fit (minimum non-utilization of cylinder space),
we must have:
Height of the cylinder = edge of the cube = \(a\)

In right angled triangle CAB:
\(CB^2\) \(=\) \(CA^2\)+\(AB^2\) \(=\) \(a^2\) + \(a^2\) \(=\) \(2a^2\)
\(=> CB =a\sqrt{2}\)
Thus, the diameter of the cylinder \(= a\sqrt{2}\)

=> Radius of the cylinder \(=\)\(\frac{a}{\sqrt{2}}\)

Thus, volume of the cylinder
\(=\) \(\pi\) X \(radius^2\) X \(height\)
\(=\) \(\pi\) X \((\frac{a}{\sqrt{2}})^2\) X \(a\)
\(= \frac{3}{2}a^3\)

Volume of the Cube \(= a^3\)
Thus, volume of the cylinder not occupied by the cube
\(=\) \(\frac{3}{2}\)\(a^3\)\(-\)\(a^3\)
\(= \frac{a^3}{2}\)

Thus, the required percent

\(= (\frac{a^3}{2})/(\frac{3}{2}a^3) X 100\)
\(=\) 33.3 %

The above situation depicts the case where minimum volume of the cylinder as a percent of the
total volume of the cylinder is unutilized, i.e. not covered by the cube.
Thus, in any other scenario, the required percent value would be either greater than or equal to
33.3%

The only possible value from the answer options is 36%

The correct answer is option E.
Attachments

Cylinder.PNG
Cylinder.PNG [ 9.5 KiB | Viewed 320 times ]

Kudos [?]: 15 [1], given: 124

Re: A solid cube is placed in a cylindrical container. Which of the follow   [#permalink] 30 Oct 2017, 22:25
Display posts from previous: Sort by

A solid cube is placed in a cylindrical container. Which of the follow

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.