Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 19 May 2013, 04:43
Customize  |  Hide

Search
Register
New posts
Unanswered

A right circular cone is inscribed in a hemisphere so that

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11514
Followers: 1791

Kudos [?]: 9531 [0], given: 826

GMAT Tests User CAT Tests
Top Member of the Month
A right circular cone is inscribed in a hemisphere so that [#permalink] New post 09 Jul 2012, 04:41
00:00

Question Stats:

65% (01:29) correct 34% (01:05) wrong based on 4 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

(A) \sqrt{3}:1

(B) 1:1

(C) \frac{1}{2}:1

(D) \sqrt{2}:1

(E) 2:1


Diagnostic Test
Question: 20
Page: 23
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11514
Followers: 1791

Kudos [?]: 9531 [0], given: 826

GMAT Tests User CAT Tests
Top Member of the Month
Re: A right circular cone is inscribed in a hemisphere so that [#permalink] New post 09 Jul 2012, 04:42
SOLUTION

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

(A) \sqrt{3}:1

(B) 1:1

(C) \frac{1}{2}:1

(D) \sqrt{2}:1

(E) 2:1

Note that a hemisphere is just a half of a sphere.

Now, since the cone is a right circular one, then the vertex of the cone must touch the surface of the hemisphere directly above the center of the base (as shown in the diagram below), which makes the height of the cone also the radius of the hemisphere.
Image

Answer: B.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Manager
Manager
Joined: 29 Mar 2012
Posts: 239
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 10

Kudos [?]: 49 [0], given: 18

GMAT ToolKit User GMAT Tests User
Re: A right circular cone is inscribed in a hemisphere so that [#permalink] New post 09 Jul 2012, 06:28
Bunuel wrote:
A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

(A) \sqrt{3}:1

(B) 1:1

(C) \frac{1}{2}:1

(D) \sqrt{2}:1

(E) 2:1

Hi,

Difficulty level: 600

As per below diagram,
Attachment:
ch.jpg
ch.jpg [ 6.18 KiB | Viewed 1252 times ]


Answer (B),

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11514
Followers: 1791

Kudos [?]: 9531 [0], given: 826

GMAT Tests User CAT Tests
Top Member of the Month
Re: A right circular cone is inscribed in a hemisphere so that [#permalink] New post 13 Jul 2012, 03:11
SOLUTION

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

(A) \sqrt{3}:1

(B) 1:1

(C) \frac{1}{2}:1

(D) \sqrt{2}:1

(E) 2:1

Note that a hemisphere is just a half of a sphere.

Now, since the cone is a right circular one, then the vertex of the cone must touch the surface of the hemisphere directly above the center of the base (as shown in the diagram below), which makes the height of the cone also the radius of the hemisphere.
Attachment:
Cone.png
Cone.png [ 23.74 KiB | Viewed 1204 times ]


Answer: B.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Re: A right circular cone is inscribed in a hemisphere so that   [#permalink] 13 Jul 2012, 03:11
    Similar topics Author Replies Last post
Similar
Topics:
 New posts There are two right circular cylinders, A and B. The joyce 1 09 Feb 2007, 22:29
Popular new posts 4 EXPERTS_POSTS_IN_THIS_TOPIC A right circular cone, twice as tall as it is wide at its andrewng 11 07 Oct 2009, 00:31
New posts 3 EXPERTS_POSTS_IN_THIS_TOPIC A right circular cone is inscribed in a hemisphere so that NvrEvrGvUp 6 03 Apr 2012, 16:49
New posts EXPERTS_POSTS_IN_THIS_TOPIC The base of a hemisphere is inscribed in one face of a cube alchemist009 3 10 Jun 2012, 17:43
New posts EXPERTS_POSTS_IN_THIS_TOPIC A right circular cylinder santivilla 2 15 Jul 2012, 12:48
Display posts from previous: Sort by

A right circular cone is inscribed in a hemisphere so that

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: Bunuel, VeritasPrepKarishma, IanStewart

Search for:


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com