GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Dec 2019, 22:35

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.

Close

Request Expert Reply

Confirm Cancel

A cylinder is placed inside a cube so that it stands upright when the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59725
A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 28 Sep 2016, 02:45
4
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:16) correct 34% (02:34) wrong based on 280 sessions

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 05 Jun 2015
Posts: 75
Location: United States
WE: Engineering (Transportation)
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 28 Sep 2016, 18:46
3
2
Volume of cube = \(s^{3}\) = 16
Volume of cylinder = \(π r^{2} h\)
To get maximum volume, we need to maximize \(r^{2}\)
Let the cylinder rest on one of the sides and the base fits completely on the surface.

We have Diameter of cylinder = side of cube
2r = s
Let the cylinder fit in he cube vertically, maximizing the height.
h = s

Volume = \(π \frac{(s}{2)}^{2} s\)
= \(\frac{π}{4} s^{3}\)
=\(\frac{π}{4} * 16\)
= \(4π\)
General Discussion
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 26 Apr 2017, 15:56
1
volume of cube is 16.
that means that a side of a cube is 3rd radical of 16, or 16 ^ (1/3)
volume of a cylinder is pi * r^2 * h
h is side of the cube
r is half of the side - [16 ^ (1/3)]/2

r^2 = 16^ (2/3)/4
we now have everything we need:
r^2 * h = [16^(2/3) * 16^(1/3)]/4 -> exponents are added and we get 16^1, which is 16.
16/4 = 4.
4*pi = 4pi.
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2552
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 26 Apr 2017, 20:26
Great Question.
Here is what i did =>
Let the side of cube =x

x^3=16

Radius of cylinder => x/2
Height => x

Hence Volume => π*r^2*h=> π*(x^2/4)*x => π*x^3/4
Putting x^3=16 we get => π*16/4 => 4π


SMASH THAT D

_________________
Intern
Intern
avatar
B
Joined: 23 Aug 2016
Posts: 47
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 30 Apr 2017, 14:24
I solved this in a pretty janky way.

I took the cubed root of 16 to be 5/2 = side of the cube and diameter of the cylinder.
Volume of a cylinder = pi (r^2) h
V = pi (5/2 * 1/2)^2 * (5/2) ... Note: the height of the cylinder is equal to the side of the cube, so again = 5/2
V = 125/32 (pi) = approximately 4 pi.
Current Student
avatar
G
Joined: 04 Jan 2016
Posts: 163
Location: United States (NY)
GMAT 1: 620 Q44 V32
GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
GPA: 3.48
GMAT ToolKit User
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 13 Jun 2017, 19:12
Well, i just looked at this question literally,
Considering that maximum volume will be achieved if the measures of the cylinder (the area of circular base and the height) need to be as close to that of the cube, in such a way that i could touch upper and lover surface and its sides heights are touch the surface the cube, then the cylinder can not have more than 16 unknown unit. Therefore, out of the options provided only option D, 4 pi was close enough to 16.
Had it been option C, then there would be enough space of two cylinder.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 20 Jun 2017, 07:37
2
Bunuel wrote:
A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described?

A. 16/π
B. 2π
C. 8
D. 4π
E. 8π


The cylinder of the maximum volume that can be inscribed in a cube is one with the diameter of its base being the side length of the cube and the height also being the side length of the cube. Recall that the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. If s = side length of the cube, we have r = s/2 (since s is also the length of the diameter) and h = s. Thus, the maximum volume of the cylinder is:

V = π*(s/2)^2*(s)

V = π(s^3)/4

Notice that s^3 is the volume of the cube and it’s given to be 16; thus, the maximum volume of the cylinder is:

V = π(16)/4

V = 4π

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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.

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4155
Location: Canada
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 13 Dec 2017, 08:00
2
Top Contributor
1
Bunuel wrote:
A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described?

A. 16/π
B. 2π
C. 8
D. 4π
E. 8π


The volume of the cube is 16
Volume of cube = (side length)³
So: 16 = (side length)³
So, side length = ∛16

So, the BASE of the cube is a SQUARE with dimension ∛16 by ∛16
So, the largest cylinder to fit inside the cube must have a diameter of ∛16
This means the RADIUS of the cylinder = ∛16/2

Also, since the cube has HEIGHT ∛16, the largest cylinder to fit inside the cube must have a HEIGHT of ∛16

What is the maximum possible volume of the cylinder that fits inside the cube as described?
Volume = π(radius)²(height)
= π(∛16/2)²(∛16)
= π(16/4)
= 4π
= D

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13737
Re: A cylinder is placed inside a cube so that it stands upright when the  [#permalink]

Show Tags

New post 20 Dec 2018, 10:45
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 Club Bot
Re: A cylinder is placed inside a cube so that it stands upright when the   [#permalink] 20 Dec 2018, 10:45
Display posts from previous: Sort by

A cylinder is placed inside a cube so that it stands upright when the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne