Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 229
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35

What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
Updated on: 02 Oct 2015, 11:38
Question Stats:
53% (02:15) correct 47% (02:20) wrong based on 90 sessions
HideShow timer Statistics
What is the radius of the largest sphere that can fit inside a right circular cone of base radius \(6 m\) and slant height \(12 m\)? A. \(2 m\) B. \(2\sqrt{3} m\) C. \(4\sqrt{3} m\) D. \(6 m\) E. \(6\sqrt{3} m\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all...  Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain
Originally posted by arhumsid on 02 Oct 2015, 10:33.
Last edited by ENGRTOMBA2018 on 02 Oct 2015, 11:38, edited 1 time in total.
Renamed the topic



CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
02 Oct 2015, 11:02
arhumsid wrote: What is the radius of the largest sphere that can fit inside a right circular cone of base radius \(6 m\) and slant height \(12 m\)?
A. \(2 m\) B. \(2\sqrt{3} m\) C. \(4\sqrt{3} m\) D. \(6 m\) E. \(6\sqrt{3} m\) Follow posting guidelines (link in my signatures).This problem is easy to solve when you convert the seemingly "3D" question into a representative 2D problem of maxium radius of the circle inside a triangle. The radius will be maximum when the triangle is equilateral triangle and the circle will be the incircle of the triangle. As shown in the attached figure, OE=OD=radius of the incircle and triangle ABC is an equialteral triangle with OD \(\perp\) BC. Thus the triangle ODC is a 306090 triangle and as BD=DC=6, \(\frac{OD}{CD} = \frac{1}{\sqrt{3}}\), giving you \(OD = 2\sqrt{3}\) B is the correct answer.
Attachments
100215 14525 PM.jpg [ 13.71 KiB  Viewed 43273 times ]



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
02 Oct 2015, 20:56
arhumsid wrote: What is the radius of the largest sphere that can fit inside a right circular cone of base radius \(6 m\) and slant height \(12 m\)?
A. \(2 m\) B. \(2\sqrt{3} m\) C. \(4\sqrt{3} m\) D. \(6 m\) E. \(6\sqrt{3} m\) Height of Cone = \(\sqrt{(12^2)  (6^2)} = \sqrt{(144)  (36)} = \sqrt{108}= 6\sqrt{3}\) Radius of Sphere = (1/3)Height = \((1/3)6\sqrt{3}\) = \(2\sqrt{3}\) Answer: option B
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 229
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
02 Oct 2015, 23:14
GMATinsight wrote: arhumsid wrote: Radius of Sphere = (1/3)Height = \((1/3)6\sqrt{3}\) = \(2\sqrt{3}\)
Im sorry, i did not get Radius of Sphere = (1/3)Height. Could you please explain how can we arrive at above relationship? Thanks!
_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all...  Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
02 Oct 2015, 23:46
arhumsid wrote: GMATinsight wrote: arhumsid wrote: Radius of Sphere = (1/3)Height = \((1/3)6\sqrt{3}\) = \(2\sqrt{3}\)
Im sorry, i did not get Radius of Sphere = (1/3)Height. Could you please explain how can we arrive at above relationship? Thanks! (Both) Slant Height = 12 Radius = 6 i.e. base Diameter = 12 i.e. In 2 Dimension the Cone is like an Equilateral Triangle in which we can derive the radius as follows
Attachments
File comment: www.GMATinsight.com
Derivation.jpg [ 132.63 KiB  Viewed 43103 times ]
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



VP
Joined: 12 Dec 2016
Posts: 1492
Location: United States
GPA: 3.64

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
10 Jan 2018, 03:27
GMATinsight, Bunuelit seems that this math problem is beyond the scope of GMAT geometry because the problem requires outside knowledge. Do you agree with me?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
10 Jan 2018, 10:35
arhumsid wrote: What is the radius of the largest sphere that can fit inside a right circular cone of base radius \(6 m\) and slant height \(12 m\)?
A. \(2 m\) B. \(2\sqrt{3} m\) C. \(4\sqrt{3} m\) D. \(6 m\) E. \(6\sqrt{3} m\) You can use the properties of equilateral triangle, if you remember them. Imagine cutting a vertical cross section of the cone with a sphere inscribed in it. The front will look like the figure above ( https://gmatclub.com/forum/whatisthe ... l#p1580927) The radius of the cone is 6 so the base of the triangle is 12. The slant height of the cone is 12 so both other sides are also 12. Hence it is an equilateral triangle. In an equilateral triangle, the inradius is \(s*\sqrt{3}/6 = 12*\sqrt{3}/6 = 2*\sqrt{3}\) Answer (B)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



VP
Joined: 12 Dec 2016
Posts: 1492
Location: United States
GPA: 3.64

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
10 Jan 2018, 11:58
VeritasPrepKarishma wrote: arhumsid wrote: What is the radius of the largest sphere that can fit inside a right circular cone of base radius \(6 m\) and slant height \(12 m\)?
A. \(2 m\) B. \(2\sqrt{3} m\) C. \(4\sqrt{3} m\) D. \(6 m\) E. \(6\sqrt{3} m\) You can use the properties of equilateral triangle, if you remember them. Imagine cutting a vertical cross section of the cone with a sphere inscribed in it. The front will look like the figure above ( https://gmatclub.com/forum/whatisthe ... l#p1580927) The radius of the cone is 6 so the base of the triangle is 12. The slant height of the cone is 12 so both other sides are also 12. Hence it is an equilateral triangle. In an equilateral triangle, the inradius is \(s*\sqrt{3}/6 = 12*\sqrt{3}/6 = 2*\sqrt{3}\) Answer (B) sure, even if the ath problem gives a very special scenario, I believe this question emphasizes too much on the 3D geometry.



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
11 Jan 2018, 02:22
chesstitans wrote: GMATinsight, Bunuelit seems that this math problem is beyond the scope of GMAT geometry because the problem requires outside knowledge. Do you agree with me? Hi chesstitansThis question may be solved by the properties that GMAT expects from tests takers hence I wouldn't discount the possibility of such a question to appear in gMAT however I will assign a very low probability for such question to appear in exam as it's too complex and also uses a solid rarely used by GMAT I.e. Cone Posted from my mobile device
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



NonHuman User
Joined: 09 Sep 2013
Posts: 13259

Re: What is the radius of the largest sphere that can fit inside a right c
[#permalink]
Show Tags
16 Jun 2019, 23:35
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 radius of the largest sphere that can fit inside a right c
[#permalink]
16 Jun 2019, 23:35






