• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

rectangular wooden box

tagged by: Brent@GMATPrepNow

rectangular wooden box

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

In this question Area could be max when radius = 5 and height = 8

A= 3.14 *25*8 = 100 * 3.14

Is it ? Then answer should be C but OA is B.

_________________
Thanks & Regards
vishalwin
------------------------------------
GMAT Score - 530
I will BEAT the GMAT!

Legendary Member
Joined
03 Feb 2014
Posted:
2063 messages
Followed by:
133 members
955
GMAT Score:
800
If the radius were 5, the cylinder would not fit inside the box.

The biggest face of the box is 8 x 10.

A circle with a radius of 5 has a diameter of 10, or is 10 wide, in all directions. So, a cylinder with a radius 5 would therefore not fit in a box unless at least one face of that box were to have dimensions of at least 10 x 10.

Given that you are constrained by either width 8, on the 8 x 10 end, or width 6, on the 6 x 8 or the 6 x 10 end, the greatest two diameters possible are 8 and 6, and the greatest two radii possible are 8/2 = 4 and 6/2 = 3.

Formula for the volume of a cylinder: π x r² x Height

Radius 3 on the 6 x 10 end generates π x 3² x 8 = 72π (You don't really need to calculate this one as the next one will have the same radius and a greater height, and so the next will will obviously have a greater volume.)

Radius 3 on the 6 x 8 end generates π x 3² x 10 = 90π

Radius 4 on the 8 x 10 end generates π x 4² x 6 = 96π

So the correct answer is B.

_________________
Marty Murray
GMAT Coach
m.w.murray@hotmail.com
https://infinitemindprep.com/
In Person in the New York Area and Online Worldwide

Last edited by Marty Murray on Wed Nov 25, 2015 7:52 am; edited 2 times in total

GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12122 messages
Followed by:
1237 members
5254
GMAT Score:
770
vishalwin 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

There are 3 different ways to position the cylinder (with the base on a different side each time).
You can place the base on the 6x8 side, on the 6x10 side, or on the 8x10 side

If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3^2)(10), which equals 90(pi)

If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3^2)(8), which equals 72(pi)

If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8).
So, the volume of this cylinder will be (pi)(4^2)(6), which equals 96(pi)

So, the greatest possible volume is 96(pi) and this occurs when the radius is 4

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
9762 messages
Followed by:
487 members
2867
GMAT Score:
800
Hi vishalwin,

You have to be careful with how you set-up this question (drawing pictures would likely help though). Since none of the sides of the box is a square, the diameter of the cylinder is limited by the SHORTER dimension of the side that is face down.

For example, if the 6x8 side was face down, then the cylinder would have a maximum diameter of 6. That limitation holds true with the other two options as well (6x10 face down ---> max diameter = 6; 8x10 face down --> max diameter = 8). Keeping that in mind, what answer would you get if you solved as normal?

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

Master | Next Rank: 500 Posts
Joined
13 Nov 2015
Posted:
137 messages
Followed by:
2 members
1
Vishalwin,

the cylinder could be placed on one of three sides: 6x8 , 6x10 , 8x10
however you need to notice that the diameter of the cylinder will be constrained by the smaller side
for example if it is placed on the side 6x8, the diameter can't be 8, because the other dimension of the box is 6, so the cylinder won't fit in; hence, we are constrained by the smaller side in every case of the three cases.

so lets consider case 1: 6x8

maximum diameter here will be 6 so radius is 3, and height is the other dimension of the box which is 10
so the volume will be 9pix10 = 90 pi

case 2: 6x10

we are constrained by the smaller dimension, 6, which will be the maximum diameter for the cylinder.

radius will still be 3, so volume will be 9pi x 8 = 72pi --> here 8 is the third dimension of the box

case 3: 8x10

the maximum diameter can be 8, so radius will be 4
volume equal: 16pi x 6 = 92pi

i hope you got it

cheers

vishalwin 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

In this question Area could be max when radius = 5 and height = 8

A= 3.14 *25*8 = 100 * 3.14

Is it ? Then answer should be C but OA is B.

GMAT/MBA Expert

GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
625
Target GMAT Score:
V51
GMAT Score:
780
The idea is right, but try drawing a circle with diameter 10 inside an 8x10 rectangle and you'll see what goes wrong. I run into this issue myself sometimes, and drawing a figure to scale usually clears things up.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

Top First Responders*

1 Jay@ManhattanReview 81 first replies
2 Brent@GMATPrepNow 71 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 fskilnik

GMAT Teacher

202 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

163 posts
3 Scott@TargetTestPrep

Target Test Prep

118 posts
4 Jay@ManhattanReview

Manhattan Review

94 posts
5 Max@Math Revolution

Math Revolution

94 posts
See More Top Beat The GMAT Experts