BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Rectangular Crate

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sun Jul 15, 2012 12:03 pm
Location: New York, USA
Thanked: 34 times
Followed by:1 members

Rectangular Crate

by kartikshah » Mon Jul 16, 2012 3:58 am
A certain rectangular crate measures 08 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed in one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

1. 4
2. 5
3. 6
4. 8
5. 10

Thanks!
Source: Princeton Review Practice Test 10
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Mon Jul 16, 2012 6:16 am
Refer to the post here >> https://www.beatthegmat.com/tough-geomet ... tml#478180
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 134
Joined: Fri Apr 06, 2012 3:11 am
Thanked: 35 times
Followed by:5 members

by Shalabh's Quants » Tue Jul 17, 2012 6:09 am
kartikshah wrote:A certain rectangular crate measures 08 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed in one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

1. 4
2. 5
3. 6
4. 8
5. 10

Thanks!
Source: Princeton Review Practice Test 10
As you are aware that Volume of a Cylinder V=Pie.r^2.h; where r= radius= diameter/2, & h= height.

So the objective is to maximise V or maximise(Pie.r^2.h);

Here Pie is constant.There are 2 variables r, & h need to be calculated.

We can also observe that Volume is proportional to height, but it is proportional to square of radius.

So the aim to assign maximum possible values out of 8,10, & 12 to radius.

Lets take 3 scenarios...

Case 1- Base is 8*10--- This option will render radius as 4 (8/2);

Case 2- Base is 12*10--- This option will render radius as 5 (10/2);

Case 3- Base is 8*12--- This option will render radius as 4 (8/2);

It is obvious that largest volume is possible if we make base as 12*10, & height as 8 ft.

So radius would be 5 ft., & Max. Volume = pie.5^2.8 = 200 cubic feet.
Shalabh Jain,
e-GMAT Instructor
Top
Post new topic Post Reply
• Page 1 of 1