GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Jan 2020, 04:12

### 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

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

# What is the volume of the largest cylinder that can fit into a box of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60484
What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 00:24
00:00

Difficulty:

(N/A)

Question Stats:

57% (01:56) correct 43% (01:21) wrong based on 37 sessions

### HideShow timer Statistics

What is the volume of the largest cylinder that can fit into a box of dimensions 6 by 8 by 10?

A. 480
B. 160π
C. 270
D. 96π
E. 90

_________________
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1045
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 00:34
Volume of a Cylinder is Pi$$r^2$$h

Lets consider 10 as the diameter of the cylinder. radius becomes 5.

height becomes 8.

Then Volume = Pi*25*8 = 200Pi.

Is my ans wrong?
Intern
Joined: 27 Jul 2018
Posts: 4
Re: What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 03:17
Afc0892 wrote:
Volume of a Cylinder is Pi$$r^2$$h

Lets consider 10 as the diameter of the cylinder. radius becomes 5.

height becomes 8.

Then Volume = Pi*25*8 = 200Pi.

Is my ans wrong?

You are taking length of box as 10, then width also needs to be at least 10 so that the cylinder fits the box, which is not the case in the given question.
You can take length as 8, so that radius=4. We should take width as 10 to fit the cylinder and height would be 6.

Then height=6
Volume= pi*4*4*6= 96*pi

If we take another case, in which we take length as 8 and 6, so that diameter=6, then height of cylinder=10

Then volume in this case:
V= pi * 3*3*10=90*pi

Hence 96*pi is the largest volume.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2981
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 05:32
Bunuel wrote:
What is the volume of the largest cylinder that can fit into a box of dimensions 6 by 8 by 10?

A. 480
B. 160π
C. 270
D. 96π
E. 90

Dimesion of box = 6 by 8 by 10

for Cylinder to have maximum volume teh radius should be as large as possible

If the circular face of cylinder is placed on the face of box with dimension 8x10 then the diameter of cylinder may be 8 at the most

i.e. Radius = 8/2 = 4 and height = 6
Volume $$= πr^2*h = π*4^2*6 = 96π$$

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2981
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 05:37
1
Afc0892 wrote:
Volume of a Cylinder is Pi$$r^2$$h

Lets consider 10 as the diameter of the cylinder. radius becomes 5.

height becomes 8.

Then Volume = Pi*25*8 = 200Pi.

Is my ans wrong?

Afc0892

Yes, Your answer is wrong because of circular face lies on the rectangular face of dimension 6x10 then the maximum diameter may be 6 if height is taken as 8
There are three cases

1) Circular face of cylinder lies on face with dimension 6x8, then Diameter = 6 and Height = 10, Now Volume $$= π*r^2*h = π*3^2*10 = 90π$$

2) Circular face of cylinder lies on face with dimension 6x10, then Diameter = 6 and Height = 8, Now Volume $$= π*r^2*h = π*3^2*8 = 72π$$

3) Circular face of cylinder lies on face with dimension 8x10, then Diameter = 8 and Height = 6, Now Volume $$= π*r^2*h = π*4^2*6 = 96π$$

I hope this helps!!!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1045
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

12 Sep 2018, 05:40
GMATinsight wrote:
Afc0892 wrote:
Volume of a Cylinder is Pi$$r^2$$h

Lets consider 10 as the diameter of the cylinder. radius becomes 5.

height becomes 8.

Then Volume = Pi*25*8 = 200Pi.

Is my ans wrong?

Afc0892

Yes, Your answer is wrong because of circular face lies on the rectangular face of dimension 6x10 then the maximum diameter may be 6 if height is taken as 8
There are three cases

1) Circular face of cylinder lies on face with dimension 6x8, then Diameter = 6 and Height = 10, Now Volume $$= π*r^2*h = π*3^2*10 = 90π$$

2) Circular face of cylinder lies on face with dimension 6x10, then Diameter = 6 and Height = 8, Now Volume $$= π*r^2*h = π*3^2*8 = 72π$$

3) Circular face of cylinder lies on face with dimension 8x10, then Diameter = 8 and Height = 6, Now Volume $$= π*r^2*h = π*4^2*6 = 96π$$

I hope this helps!!!

Understood. Thanks sir.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9053
Location: United States (CA)
Re: What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

14 Sep 2018, 17:41
Bunuel wrote:
What is the volume of the largest cylinder that can fit into a box of dimensions 6 by 8 by 10?

A. 480
B. 160π
C. 270
D. 96π
E. 90

The largest cylinder that will fit into a box of dimensions 6 by 8 by 10 will have the diameter of its base equal to one of the dimensions of the box and the height equal to another dimension of the box. Furthermore, if the base of the cylinder rests on a face of the box that is a by b, then the diameter of the base can’t exceed the lesser of a and b. For example, if the base of the cylinder rests on a face of the box that is 6 by 8, then the diameter of the base can’t exceed 6. With this in mind, let’s explore all the possible options of the volume of the cylinder. Recall that the volume of a cylinder is V = πr^2h

1) The base rests on a face that is 6 by 8; thus, the diameter = 6 and hence the radius = 3 and height = 10.

V = π(3)^2(10) = 90π

2) The base rests on a face that is 6 by 10; thus, the diameter = 6 and hence the radius = 3 and height = 8.

V = π(3)^2(8) = 72π

3) The base rests on a face that is 8 by 10; thus, the diameter = 8 and hence the radius = 4 and height = 6.

V = π(4)^2(6) = 96π

We see that 96π is the largest possible volume for the cylinder.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13976
Re: What is the volume of the largest cylinder that can fit into a box of  [#permalink]

### Show Tags

04 Dec 2019, 05:29
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.
_________________
Re: What is the volume of the largest cylinder that can fit into a box of   [#permalink] 04 Dec 2019, 05:29
Display posts from previous: Sort by