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

It is currently 11 Jul 2014, 12:54

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

a rectangular box has 12 x 10 x 8 dimensions. what is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2772
Location: New York City
Followers: 6

Kudos [?]: 185 [0], given: 4

GMAT Tests User
a rectangular box has 12 x 10 x 8 dimensions. what is the [#permalink] New post 18 Apr 2007, 15:50
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?
VP
VP
User avatar
Joined: 03 Apr 2007
Posts: 1378
Followers: 2

Kudos [?]: 147 [0], given: 10

GMAT Tests User Reviews Badge
Re: volume question [#permalink] New post 18 Apr 2007, 17:13
bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?



The 3 surfaces are: 12*10,12*8,8*10

AMong the three 12*10 has the largest surface area. It can fit a cylinder of maximum diameter 10. Hence radius =5

V = pi*r^2*h= 25*9pi= 200pi

You can verify with other options:
For 12*8: r = 4, V=160pi
For 8*10:r =4,V=192pi
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1157
Followers: 6

Kudos [?]: 105 [0], given: 0

GMAT Tests User
re: Box [#permalink] New post 18 Apr 2007, 23:21
look in the diagram showing the box - the blue circle has diameter of 10 and the yellow circle a diameter of 12 - you will have to compromise and "lose" space in order to squeeze in the blue circle but you can't squeeze in the yellow one.

if you will pick 6 as the radius of the cylinder, the cylinder will not fit into the box (as shown in the diagram).

other options are far worse:

10*12 = you have to pick 5 as radius.

12*8 = you have to pick 4 as radius.

8*10 = you have to pick 4 as radius.

hope it helps :-D
Attachments

untitled.JPG
untitled.JPG [ 8.78 KiB | Viewed 529 times ]

Manager
Manager
avatar
Joined: 04 Oct 2006
Posts: 78
Followers: 1

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

Re: volume question [#permalink] New post 01 May 2007, 05:41
bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


You have to take in consideration the radius and the hight of the cylinder. Then 6 is not the largest radius that gives the largest volume.
Senior Manager
Senior Manager
User avatar
Joined: 24 Nov 2006
Posts: 352
Followers: 1

Kudos [?]: 11 [0], given: 0

GMAT Tests User
Re: volume question [#permalink] New post 01 May 2007, 08:07
In a general sense: Let a<b<c the sides of the rectangle. Then, the corresponding volumes of inscribed right cilinders would be:

pi*a^2/4*c
pi*b^2/4*a
pi*a^2/4*b

The last one is always the smallest volume. Now, between the 1st and the 2nd, it´ll depend on whether ac<>b^2. In the particular case of the question U brought about, b=10, and b^2=100 is in effect larger than 8*12=96. Had the smallest side been 9 instead of 8, we´d have had the other case: 10^2<9*12(=108).

Hope this helps.

bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2772
Location: New York City
Followers: 6

Kudos [?]: 185 [0], given: 4

GMAT Tests User
Re: re: Box [#permalink] New post 01 Jun 2007, 23:37
KillerSquirrel wrote:
look in the diagram showing the box - the blue circle has diameter of 10 and the yellow circle a diameter of 12 - you will have to compromise and "lose" space in order to squeeze in the blue circle but you can't squeeze in the yellow one.


still confused. how exactly do we compromise (in numbers please :-D)?
Director
Director
User avatar
Joined: 14 Jan 2007
Posts: 783
Followers: 2

Kudos [?]: 43 [0], given: 0

GMAT Tests User
Re: volume question [#permalink] New post 02 Jun 2007, 03:01
bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


you can't take 12 as the cylinder will not fit into box then.
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2772
Location: New York City
Followers: 6

Kudos [?]: 185 [0], given: 4

GMAT Tests User
Re: volume question [#permalink] New post 26 Sep 2007, 12:58
bmwhype2 wrote:
My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


all right. i finally figured it out after some basic reasoning. a 12 inch ball cannot fit into a 12 inch box without some slack space. Image

therefore, we take the two largest dimensions as the base and then take the smaller of the base dimensions as a radius. thereby leaving the shortest dimension of the three as the height.

there is another question like this one on the board.
http://www.gmatclub.com/forum/t40806
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 173 [0], given: 0

GMAT Tests User
Re: volume question [#permalink] New post 26 Sep 2007, 13:15
bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


got the same answer. Did this come from MGMAT?
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5097
Location: Singapore
Followers: 16

Kudos [?]: 130 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Sep 2007, 19:11
If the base is 10 * 8, then volume is pi(4^2)(12) = 192pi
If the base is 10 * 12, then volume is pi(5^2)(8) = 200pi
If the base is 12 * 8, then volume is pi(4^2)(10) = 160pi

So largest volume = 200pi
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5097
Location: Singapore
Followers: 16

Kudos [?]: 130 [0], given: 0

GMAT Tests User
Re: volume question [#permalink] New post 26 Sep 2007, 19:12
GMATBLACKBELT wrote:
bmwhype2 wrote:
a rectangular box has 12 x 10 x 8 dimensions. what is the largest possible volume of a right cylinder that is placed inside the box?

Answer:
V= (pi) (r^2) H
V= (5^2) pi x 8
V=200pi

the explanation was the radius of the cylinder must be equal to half of the smaller of the 2 dimensions of the box's bottom. the largest possible radius will yield the largest volume.

My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


got the same answer. Did this come from MGMAT?


I think I saw this question on ETS retired paper test.... can't be sure though but it does seem familiar to me.
Manager
Manager
avatar
Joined: 29 Jul 2007
Posts: 183
Followers: 1

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

GMAT Tests User
 [#permalink] New post 27 Sep 2007, 21:40
I think OG11 (PS #191) is very similar to this.
Current Student
avatar
Joined: 03 Oct 2006
Posts: 85
Followers: 1

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

GMAT Tests User
Re: volume question [#permalink] New post 24 Oct 2007, 18:44
bmwhype2 wrote:
bmwhype2 wrote:
My question is..... why didnt we take half of 12 instead of 10 since we are looking for the largest radius?


all right. i finally figured it out after some basic reasoning. a 12 inch ball cannot fit into a 12 inch box without some slack space. Image

therefore, we take the two largest dimensions as the base and then take the smaller of the base dimensions as a radius. thereby leaving the shortest dimension of the three as the height.

there is another question like this one on the board.
http://www.gmatclub.com/forum/t40806


Nice! Best explanation in this thread.

Thanks!
Re: volume question   [#permalink] 24 Oct 2007, 18:44
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic A closed aluminum rectangular box has inner dimensions x gmatbull 7 21 Oct 2012, 10:07
1 A rectangular box has the dimensions 12 inches x 10 inches x jimjohn 5 14 Oct 2007, 16:45
A rectangular box has dimensions 12 X 8 X 10. what is the Sumithra Sen 5 19 Aug 2007, 13:53
The rectangular box with 2x8x20 inches dimension is to be Himalayan 4 04 Feb 2007, 19:17
13 Experts publish their posts in the topic A rectangular box has dimensions 12*10*8 inches. What is the willget800 17 25 Apr 2006, 17:54
Display posts from previous: Sort by

a rectangular box has 12 x 10 x 8 dimensions. what is the

  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®.