Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Oct 2014, 05:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A circle is inscribed in a half circle with a diameter of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 231
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Followers: 5

Kudos [?]: 22 [0], given: 33

A circle is inscribed in a half circle with a diameter of [#permalink] New post 23 Feb 2012, 00:53
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (01:45) correct 32% (01:12) wrong based on 22 sessions
A circle is inscribed in a half circle with a diameter of \pi . What is the ratio of the area of the half circle to the area not covered by the inscribed circle?

1:1
1:2
1:4
3:4
2:1

I know this has been discussed before & answer is easy to figure out. But my doubt is how to figure out the area of the inscribed circle.
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28598 [0], given: 2803

Re: Circles [#permalink] New post 23 Feb 2012, 02:46
Expert's post
GMATPASSION wrote:
A circle is inscribed in a half circle with a diameter of \pi . What is the ratio of the area of the half circle to the area not covered by the inscribed circle?

1:1
1:2
1:4
3:4
2:1

I know this has been discussed before & answer is easy to figure out. But my doubt is how to figure out the area of the inscribed circle.


This question needs a revision, because there are infinitely many circles possible to inscribe in a semicircle. Consider just two cases below:
Attachment:
Semicircle.PNG
Semicircle.PNG [ 18.1 KiB | Viewed 1845 times ]
Now, intended meaning of the question is the case with the circle which inscribed right in the middle but it should be specified.

Anyway, for that case we don't really need any formula to get the ratio:
Since the radius of the big circle (\frac{\pi}{2}) is twice the radius of the inscribed circle (\frac{\pi}{4}) then its area is 4 times greater then the area of the inscribed circle (because in the area formula the radius is squared. For example the area of a circle with radius of 2 is 4\pi, which is 4 times greater than the radius of a circle with the radius of 1, which is \pi).

Thus the are of the semicircle is 4/2=2 times greater than the area of the inscribed circle: the area of the semicircle 2 units, the area of the inscribed circle 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1. Ratio: 2/1.

Answer: E.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 23 Jun 2011
Posts: 6
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: A circle is inscribed in a half circle with a diameter of [#permalink] New post 23 Feb 2012, 03:12
E is the answer.


The inscribed circle will have diameter equal to radius of half circle....

area of unshaded region would be = area of semi-circle - area of inscribed circle
Intern
Intern
avatar
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
Followers: 0

Kudos [?]: 0 [0], given: 12

Re: A circle is inscribed in a half circle with a diameter of [#permalink] New post 23 Feb 2012, 05:19
area of full circle is picube/4
area of half circle is picube /8

now area of circle with radius pi/4 is picube /16
area not covered by inscribed circle is picube /8 - picube /16 = picube /16

area of half circle / area not covered by inscribed circle = picube/8 divides by picube/16
which will give us ratio 2:1

answer is E
Re: A circle is inscribed in a half circle with a diameter of   [#permalink] 23 Feb 2012, 05:19
    Similar topics Author Replies Last post
Similar
Topics:
Quadrilateral ABCD is inscribed in circle K. The diameter of fozzzy 0 23 Jun 2013, 04:36
14 Experts publish their posts in the topic Quadrilateral ABCD is inscribed in circle K. The diameter of bhandariavi 16 05 Feb 2011, 17:04
inscribed circle in half circle bupbebeo 4 30 Aug 2010, 07:21
8 Experts publish their posts in the topic A rectangle is inscribed in a circle of diameter 2. Which of GK_Gmat 14 03 Jan 2008, 23:23
1 What is the diameter of the circle inscribed in an isoceles yessuresh 8 27 May 2006, 07:52
Display posts from previous: Sort by

A circle is inscribed in a half circle with a diameter of

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.