GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Dec 2019, 05:30

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

The inside dimensions of a rectangular wooden box are 4 mete

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 28 May 2009
Posts: 143
Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
GMAT ToolKit User
The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

New post 08 Mar 2013, 11:41
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:22) correct 44% (02:24) wrong based on 122 sessions

HideShow timer Statistics

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) \(100 \pi\)

_________________
Intern
Intern
avatar
Joined: 30 Oct 2012
Posts: 17
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q50 V40
WE: Science (Transportation)
Reviews Badge
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

New post 08 Mar 2013, 12:17
3
1
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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59724
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

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.
_________________
Intern
Intern
avatar
Joined: 26 Jan 2015
Posts: 3
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

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?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15729
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
VP
VP
avatar
P
Joined: 12 Dec 2016
Posts: 1485
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

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.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13739
Re: The inside dimensions of a rectangular wooden box are 4 mete  [#permalink]

Show Tags

New post 10 Aug 2019, 18:07
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: The inside dimensions of a rectangular wooden box are 4 mete   [#permalink] 10 Aug 2019, 18:07
Display posts from previous: Sort by

The inside dimensions of a rectangular wooden box are 4 mete

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





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