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

It is currently 04 Aug 2020, 04:00
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
CLICK HERE TO HIDE/SHOW EVENTS

If a sphere with radius r is inscribed in a cube with edges of length

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
First unread post
Print view
 
  Sort by Date Sort by Kudos  
Search for:
 
PREVIOUS TOPIC
NEXT TOPIC
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 515
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20, Yale '20, Tepper '20
GPA: 2.81
WE: Business Development (Real Estate)
GMAT ToolKit User
Top Member of the Month
If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post Updated on: 17 Jun 2017, 12:49
8
Top Contributor
22
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (00:53) correct 15% (01:08) wrong based on 1356 sessions

HideShow timer Statistics

If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)
Spoiler: OA

Originally posted by AbdurRakib on 17 Jun 2017, 10:06.
Last edited by Bunuel on 17 Jun 2017, 12:49, edited 1 time in total.
Edited the question.
Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 05 Dec 2016
Posts: 2
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 05 Jul 2017, 07:30
10
2
Since the side of the cube serves as the diameter of the sphere,
2r = e
r = e/2
r = 1/2 e
Attachments

File comment: visual rep of the problem
gmatclub.png
gmatclub.png [ 67.92 KiB | Viewed 26494 times ]

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
CAT Tests
Top Member of the Month
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 17 Jun 2017, 12:55
1
2
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)


A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

Answer: A.
_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
CAT Tests
Top Member of the Month
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 17 Jun 2017, 12:56
1
Bunuel wrote:
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)


A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

Answer: A.


Check other 3-D Geometry Questions in our Special Questions Directory.
_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 515
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20, Yale '20, Tepper '20
GPA: 2.81
WE: Business Development (Real Estate)
GMAT ToolKit User
Top Member of the Month
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 17 Jun 2017, 13:01
Top Contributor
Bunuel wrote:
Bunuel wrote:
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)


A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

Answer: A.


Check other 3-D Geometry Questions in our Special Questions Directory.


Thank you very much
Manager
Manager
User avatar
B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 178
Location: India
Concentration: Finance, International Business
If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 16 Jul 2017, 03:22
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
CAT Tests
Top Member of the Month
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 16 Jul 2017, 03:28
longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??


Yes. In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.
_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Intern
Intern
avatar
B
Joined: 05 Dec 2016
Posts: 2
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 16 Jul 2017, 06:43
2
longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square. Am I correct??



Sure the inscribed circle must touch all the four sides of the Rectangle so the side of the rectangle is same as the diameter. see the images attached that also show circumscribed circle, in this case the diagonal of the rectangle serves and the diameter
Attachments

dia.png
dia.png [ 89.93 KiB | Viewed 26057 times ]

Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 15 Nov 2017, 15:50
2
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)


Since the sphere is inscribed in the cube, the length of an edge of the cube = the diameter of the sphere. Recall that the diameter is twice the radius. Thus, e = 2r, or 1/2e = r.

Answer: A
_________________

★ ★ ★ ★ ★   250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

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

Signature Read More
Manager
Manager
User avatar
G
Joined: 29 Jun 2018
Posts: 53
Location: India
Schools: Johnson '20, HEC Montreal '21
GPA: 4
GMAT ToolKit User
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 23 Jun 2019, 05:44
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. \(r=\frac{1}{2}e\)

B. r = e

C. r = 2e

D. \(r=\sqrt{e}\)

E. \(r=\frac{1}{4}e^2\)


First of all, if you have a sphere that is inscribed inside of a cube,

that means that the cube's side is going to be exactly twice the radius.

So the radius is going to be half of the edge, and that's about it.

You don't need to calculate anything. The correct answer choice is A.
_________________
Ramya Seth
Article I propose this Month :
https://www.linkedin.com/pulse/standalone-machine-yet-smart-analytic-piece-iiot-puzzle-bulusu/
Signature Read More
Intern
Intern
avatar
B
Joined: 28 May 2020
Posts: 13
Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

Show Tags

New post 05 Jul 2020, 14:25
If the sphere is inscribed in a cuboid instead of a cube (i.e., sides are not of equal lengths), is it correct to say that the diameter of the sphere will be equal to the shortest length of the cuboid? Thanks!
GMAT Club Bot
Re: If a sphere with radius r is inscribed in a cube with edges of length   [#permalink] 05 Jul 2020, 14:25
Print view
First unread post

If a sphere with radius r is inscribed in a cube with edges of length

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

Moderators: chetan2u, VeritasKarishma, yashikaaggarwal, Bunuel, generis

Search for:
PREVIOUS TOPIC
NEXT TOPIC





cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions