It is currently 21 Oct 2017, 05:38

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

The inside dimensions of a rectangular wooden box are 6 inches by 8 in

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

Hide Tags

Intern
Intern
avatar
Joined: 02 Jan 2010
Posts: 5

Kudos [?]: 4 [0], given: 0

The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

Show Tags

New post 16 Jan 2010, 22:05
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

46% (01:13) correct 54% (01:21) wrong based on 61 sessions

HideShow timer Statistics

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

[Reveal] Spoiler:
This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
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.


Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-inside-d ... 28053.html
[Reveal] Spoiler: OA

Kudos [?]: 4 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 298

Kudos [?]: 150 [0], given: 6

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

Show Tags

New post 17 Jan 2010, 02:48
anil4410 wrote:
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 maximum volume?

a)3
b)4
c)5
d)6
e)8

This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
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.


Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.


The question asks for cylindrical canister which has the maximum volume ( bigger the radius bigger the volume will be V = pi r^2h)

Radius will be maximum when we the area of the base of the cuboid is maximum, options are 6 x8 , 6 x10 and 8 x 10,

Out of these if we choose first 2 options maximum diameter for the cylinder would be 6 ( or Radius as 3),
Hence the last option 8 x10, so the diameter of the cylinder becomes 8 and radius 4

I hope this will help ..!

Cheers

Kudos [?]: 150 [0], given: 6

1 KUDOS received
Manager
Manager
avatar
Joined: 26 Nov 2009
Posts: 162

Kudos [?]: 62 [1], given: 5

GMAT ToolKit User
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

Show Tags

New post 17 Jan 2010, 09:24
1
This post received
KUDOS
to have the maximum radius we should rest the wooden box with max dimensions as base

for the wooden box 6*10*8 it should rest with 10*8 as base and 6 as height .

for the given dimension 10*8 the maximum possible radius will be 4 since if radius is greater than 4 than side with dimension 8 will not be able to accomadate it

so the ans is b)3

Kudos [?]: 62 [1], given: 5

Intern
Intern
User avatar
S
Joined: 17 Jan 2016
Posts: 22

Kudos [?]: 9 [0], given: 249

Location: India
Concentration: General Management, General Management
GMAT ToolKit User Premium Member
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

Show Tags

New post 02 Mar 2017, 01:28
There are 3 possible surfaces of this cuboid where the base of the cylinder will rest.They are

a) 6 X 8 - If the cylinder is placed in this position, it's dia would be the smallest of these two. Otherwise the cylinder cannot be accommodated. It's height would be 10 inches. So volume would be - 282.

b) 8 X 10 - Dia in this case would be 8 and height - 6. So volume would be - 301.

c) 10 X 6 - Dia in this case would be 6 and height - 8. So volume here would be - 226.

Clearly the the dia would be 8 and hence the radius should be 4 for the cylinder to have maximum volume.

Kudos [?]: 9 [0], given: 249

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129094 [0], given: 12194

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

Show Tags

New post 02 Mar 2017, 05:18
anil4410 wrote:
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

[Reveal] Spoiler:
This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
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.


Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-inside-d ... 28053.html




\(volume_{cylinder}=\pi{r^2}h\)

If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*10=90\pi\);
If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*8=72\pi\);
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*6=96\pi\);

So, the maximum volume is for \(r=4\).

Answer: B.

Hope it's clear.

P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129094 [0], given: 12194

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in   [#permalink] 02 Mar 2017, 05:18
Display posts from previous: Sort by

The inside dimensions of a rectangular wooden box are 6 inches by 8 in

  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®.