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

It is currently 19 Nov 2018, 14:49

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

A cube with a volume of 64 cubic inches is inscribed within a sphere

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50670
A cube with a volume of 64 cubic inches is inscribed within a sphere  [#permalink]

Show Tags

New post 06 Jun 2017, 10:30
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:28) correct 35% (01:42) wrong based on 111 sessions

HideShow timer Statistics

A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2
B. 2π√3
C. 4π√2
D. 4π√3
E. 8π√2

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
S
Joined: 24 Dec 2016
Posts: 93
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: A cube with a volume of 64 cubic inches is inscribed within a sphere  [#permalink]

Show Tags

New post 06 Jun 2017, 21:43
2
1
1
Bunuel wrote:
A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2
B. 2π√3
C. 4π√2
D. 4π√3
E. 8π√2



In case of a cube inscribed within a sphere, the cube's diagonal (largest distance between any 2 points on the cube) and the sphere's diameter (largest distance between any 2 points on the sphere) should be equal.
We also know that the diagonal for a cube = \(\sqrt{3}*Side\)

As the volume of the cube = 64 cu. inches, its sides should be 4 inches each.
Thus diagonal = \(4\sqrt{3}\) = Diameter of the sphere.
Thus radius = \(2\sqrt{3}\)
=> Circumference of the sphere = \(2π*2\sqrt{3}\) = \(4π√3\)

Should be Option D.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A cube with a volume of 64 cubic inches is inscribed within a sphere  [#permalink]

Show Tags

New post 10 Jun 2017, 06:34
Bunuel wrote:
A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2
B. 2π√3
C. 4π√2
D. 4π√3
E. 8π√2


Since the cube is inscribed in the sphere, we know that the diagonal of the cube is equal to the diameter of the sphere.

Since the volume of the cube is 64 and volume = side^3, the side is 4. Since the diagonal of a cube is side√3, the diagonal of the cube is 4√3.

Since the sphere’s diameter = 4√3, its radius is 2√3, and thus its circumference = 2πr = 2π(2√3) = 4π√3.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4230
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: A cube with a volume of 64 cubic inches is inscribed within a sphere  [#permalink]

Show Tags

New post 26 Oct 2018, 07:02
JeffTargetTestPrep wrote:
Bunuel wrote:
A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2
B. 2π√3
C. 4π√2
D. 4π√3
E. 8π√2


Since the cube is inscribed in the sphere, we know that the diagonal of the cube is equal to the diameter of the sphere.

Since the volume of the cube is 64 and volume = side^3, the side is 4. Since the diagonal of a cube is side√3, the diagonal of the cube is 4√3.

Since the sphere’s diameter = 4√3, its radius is 2√3, and thus its circumference = 2πr = 2π(2√3) = 4π√3.

Answer: D


Certainly so, here is how the figure will look -
Attachment:
main-qimg-4fa003c3a8c93fdbba78e63d8f8c4622.png
main-qimg-4fa003c3a8c93fdbba78e63d8f8c4622.png [ 8.09 KiB | Viewed 293 times ]

Answer must be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Intern
avatar
B
Joined: 27 Nov 2017
Posts: 11
Re: A cube with a volume of 64 cubic inches is inscribed within a sphere  [#permalink]

Show Tags

New post 27 Oct 2018, 23:54
Hi Bunuel,

Sphere is 3-D object, so will there be circumference for this object or is the question asking about the projection of the sphere?
GMAT Club Bot
Re: A cube with a volume of 64 cubic inches is inscribed within a sphere &nbs [#permalink] 27 Oct 2018, 23:54
Display posts from previous: Sort by

A cube with a volume of 64 cubic inches is inscribed within a sphere

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

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®.