It is currently 11 Dec 2017, 08:28

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

Events & Promotions in June
Open Detailed Calendar

Sphere is inscribed in a cube of side length 10 cms. What is

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

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 21 Jun 2006
Posts: 282

Kudos [?]: 145 [1], given: 0

Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

Show Tags

New post 30 Jun 2007, 18:52
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (01:23) correct 55% (01:23) wrong based on 132 sessions

HideShow timer Statistics

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

(A) \(10(\sqrt{3}- 1)\)
(B) \(5\)
(C) \(10(\sqrt{2} - 1)\)
(D) \(5(\sqrt{3} - 1)\)
(E) \(5(\sqrt{2} - 1)\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-100798.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 May 2014, 03:36, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

Kudos [?]: 145 [1], given: 0

Senior Manager
Senior Manager
User avatar
Joined: 28 Feb 2007
Posts: 300

Kudos [?]: 44 [0], given: 0

 [#permalink]

Show Tags

New post 30 Jun 2007, 22:19
sh.distance=[diagonal of cube - diameter of sphere]/2

which is [10*sqrt3 - 10]/2 =5*sqrt3-5

Kudos [?]: 44 [0], given: 0

Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 45

Kudos [?]: 54 [0], given: 1

Re: Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

Show Tags

New post 21 May 2014, 09:40
Diagonal of the cube = 10*sqrt (3)
Diameter of Sphere = 10 cm

Diagonal of the cube will cross the center of sphere and it is perpendicular on the surface of sphere.

Smallest distance is the perpendicular distance from a surface

If we subtract diameter of sphere from diagonal of cube , we will get the part of diagonal which is out of the sphere.

since it contains two sides

minimum distance = (10 sqrt(3) - 10)/2 = 5*sqrt(3) - 5
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

Kudos [?]: 54 [0], given: 1

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42545

Kudos [?]: 135229 [0], given: 12674

Re: Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

Show Tags

New post 22 May 2014, 03:37
Expert's post
4
This post was
BOOKMARKED
A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
(A) \(10(\sqrt{3}- 1)\)
(B) \(5\)
(C) \(10(\sqrt{2} - 1)\)
(D) \(5(\sqrt{3} - 1)\)
(E) \(5(\sqrt{2} - 1)\)

Shortest distance=(diagonal of cube-diameter of sphere)/2= \(\frac{10*\sqrt{3}-10}{2}=5(\sqrt{3}-1)\)

Answer: D.

Similar questions to practice:
a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-127461.html
a-rectangular-box-has-dimensions-of-8-feet-8-feet-and-z-128483.html
for-the-cube-shown-above-what-is-the-degree-measure-of-pqr-13841.html
a-rectangular-box-is-10-inches-wide-10-inches-long-and-144733.html
if-the-box-shown-is-a-cube-then-the-difference-in-length-127463.html
what-is-the-volume-of-the-cube-above-103680.html
if-a-cube-is-inscribed-inside-a-sphere-154770.html

3-D Geometry Questions Directory: 3-d-geometry-questions-171024.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-100798.html
_________________

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

Kudos [?]: 135229 [0], given: 12674

Re: Sphere is inscribed in a cube of side length 10 cms. What is   [#permalink] 22 May 2014, 03:37
Display posts from previous: Sort by

Sphere is inscribed in a cube of side length 10 cms. What is

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.