Find all School-related info fast with the new School-Specific MBA Forum

It is currently 04 Sep 2015, 22:10
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 17 Feb 2010
Posts: 14
Followers: 0

Kudos [?]: 3 [0], given: 3

The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 17 Mar 2010, 17:30
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:02) correct 46% (01:26) wrong based on 110 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Apr 2015, 02:47, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 117 [0], given: 5

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 17 Mar 2010, 19:02
hb05sv wrote:
Can someone show me how to solve the following question?


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

Correct Ans is B.


let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area.
so B - 4
Senior Manager
Senior Manager
User avatar
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 16

Kudos [?]: 119 [0], given: 22

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 17 Mar 2010, 19:26
kp1811 wrote:
let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area.
so B - 4


Nice explanation -

To be more specific, logically, for any face down of the cube, the smaller length only can be the diameter of the cylindrical canister. So either ways, it is 6 or 8. The height will be either the shortest or the longest dimension accordingly.

Volume of cylinder is Pi * r squared * h. The greater the value of r^2*h, the greater the volume.
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

Intern
Intern
avatar
Joined: 17 Feb 2010
Posts: 14
Followers: 0

Kudos [?]: 3 [0], given: 3

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 18 Mar 2010, 14:23
BarneyStinson, Can you explain why logically the diameter of the cylinder will be one of the shortest?
Senior Manager
Senior Manager
User avatar
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 16

Kudos [?]: 119 [0], given: 22

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 18 Mar 2010, 16:04
hb05sv wrote:
BarneyStinson, Can you explain why logically the diameter of the cylinder will be one of the shortest?


Because if the diameter were wider say 8", it won't fit into a box that has one side 6", when the face down is 8" X 6".
You should definitely read my blog!!!
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

1 KUDOS received
Manager
Manager
avatar
Joined: 23 Apr 2010
Posts: 138
Location: Tx
Schools: NYU,UCLA,BOOTH,STANFORD
Followers: 1

Kudos [?]: 43 [1] , given: 36

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 20 Aug 2010, 06:22
1
This post received
KUDOS
kp1811 wrote:
hb05sv wrote:
Can someone show me how to solve the following question?


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

Correct Ans is B.


let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area.
so B - 4


Sorry guyz but dont understand your ways

My approach is;

pi approx. = 3,14

The box volume is 480 so;

Cylinder max. volume should be pi*5^2*8 = 200pi means more then 600 so cant be, If the radius cant be 5 so it should be 4;

pi*4^2*10= slightly more then 480 so CANT BE

then the answer is;

pi*4^2*6 < 480 it means The radius should be "4".


B
_________________

This is not finished here...Watch me.....

1 KUDOS received
Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 240
Location: Hyderabad
WE 1: 4.6 years Exp IT prof
Followers: 8

Kudos [?]: 31 [1] , given: 48

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 21 Aug 2010, 15:17
1
This post received
KUDOS
Since we want Max Volume for cylinder hence Max Vol can only max if the Radius is maximum

We can always have Cylinder with radius 3 in this Box but we need max radius if we take (6 and 8) or (6 and 10) or (10 and 8)

So let us pick 5 as radius so the diameter will be 10 but other two sides are 8 and 6 which cause a cylinder with 10 radius out of the box. Hence 5 is not the answer
Anything above 5 i.e 6 and 8 are gone
Now we come to our last option 4 if we take sides 10 and 8 as the base we can surely incorporate cylinder inside the box hence our answer is B i.e. 4.

Try to give it a thought because I have not used any calculation to solve this question.
And don't forget in Gmat Exam we need to conserve all our energies because after Quants exam the beast awaits......VERBAL!!!!!!
_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Don't Forget to give the KUDOS

Senior Manager
Senior Manager
User avatar
Joined: 18 Jun 2010
Posts: 302
Schools: Chicago Booth Class of 2013
Followers: 22

Kudos [?]: 158 [0], given: 194

Reviews Badge
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 31 Aug 2010, 10:15
amneetpadda wrote:
And don't forget in Gmat Exam we need to conserve all our energies because after Quants exam the beast awaits......VERBAL!!!!!!


And remember to reserve some extra energy for AWA:)
Manager
Manager
avatar
Joined: 16 Mar 2010
Posts: 189
Followers: 2

Kudos [?]: 79 [0], given: 9

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 31 Aug 2010, 23:34
Calculate r^2 * h for all cases you gat the answer
Manager
Manager
avatar
Joined: 16 May 2011
Posts: 204
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Followers: 1

Kudos [?]: 47 [0], given: 37

GMAT ToolKit User
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 01 Jun 2011, 04:08
6*8*10-hence:
side 6*8 r=3 h=10
side 6*10 r=3 h=8
side 8*10 r=4 h=6

pir^2 will be bigger at side 8*10
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1356
Followers: 14

Kudos [?]: 178 [0], given: 10

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 13 Jun 2011, 00:15
l = 10,w = 8 and h = 6
gives max volume.

r = 4.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Intern
Intern
avatar
Joined: 24 Jul 2011
Posts: 2
Followers: 0

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

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 23 Nov 2011, 08:40
The above mentioned solutions are correct, but from my perspective the question could be misleading (at least for non-natives).
The question states "a cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on (ANY) one of its six faces".
Since the canister has a fixed volume and we cannot be sure on which face the wooden box will stand, we would have to assume that it could also stay on the smallest possible area, namely 6 by 8.
If so, the correct solution, 4, would be wrong, since the diameter would exceed the side length 6.
Sorry if I confused you guys, but I personally dislike such questions, since they inhabit the potential for incorrect choices only due to the unclear phrasing of the question.

My 2 cents.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6221
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 14 Apr 2015, 16:44
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50385 [0], given: 7544

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 15 Apr 2015, 02:48
Expert's post
hb05sv 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


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

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50385 [0], given: 7544

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink] New post 15 Apr 2015, 02:48
Expert's post
Bunuel wrote:
hb05sv 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


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

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.



Similar questions to practice:
the-inside-of-a-rectangular-carton-is-48-centimeters-long-138301.html
a-rectangular-box-has-dimensions-12-10-8-inches-what-is-the-28790.html
a-closed-cylindrical-tank-contains-36pi-cubic-feet-of-water-134500.html
what-is-the-number-of-cans-that-can-be-packed-in-a-certain-143776.html
a-cylindrical-tank-of-radius-r-and-height-h-must-be-redesign-122366.html
a-rectangular-box-has-dimensions-12-10-8-inches-what-is-the-28790.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in   [#permalink] 15 Apr 2015, 02:48
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic The inside dimensions of a rectangular wooden box are 4 mete megafan 5 08 Mar 2013, 10:41
6 Experts publish their posts in the topic A rectangular box has dimensions of 8 feet, 8 feet, and z enigma123 3 02 Mar 2012, 14:53
16 Experts publish their posts in the topic The inside dimensions of a rectangular wooden box are 6 BANON 9 23 Feb 2012, 22:20
7 Experts publish their posts in the topic The dimensions of a rectangular solid are 4 inches, 5 inches nusmavrik 15 20 Aug 2010, 23:20
24 Experts publish their posts in the topic A rectangular box has dimensions 12*10*8 inches. What is the willget800 18 25 Apr 2006, 17:54
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.