Last visit was: 12 Dec 2024, 05:36 It is currently 12 Dec 2024, 05:36
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
Back to Forum
Create Topic
555-605 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 Dec 2024
Posts: 97,842
Own Kudos:
685,262
 [4]
Given Kudos: 88,254
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,842
Kudos: 685,262
 [4]
In the figure above, if semicircles A and B each have area 4pi 15 Mar 2018, 23:57
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:46) correct 25% (01:53) wrong based on 167 sessions

History

Date
Time
Result
Not Attempted Yet


In the figure above, if semicircles A and B each have area \(4\pi\), what is the area of semicircle C?


(A) \(4\pi\)

(B) \(4\pi \sqrt{2}\)

(C) \(6\pi\)

(D) \(8\pi\)

(E) 16


Show Spoiler
Attachment:
2018-03-16_1011_003.png
2018-03-16_1011_003.png [ 9.14 KiB | Viewed 4481 times ]
ShowHide Answer
Official Answer
D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 Dec 2024
Posts: 97,842
Own Kudos:
685,262
 [2]
Given Kudos: 88,254
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,842
Kudos: 685,262
 [2]
In the figure above, if semicircles A and B each have area 4pi 15 Mar 2018, 23:57
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel


In the figure above, if semicircles A and B each have area \(4\pi\), what is the area of semicircle C?


(A) \(4\pi\)

(B) \(4\pi \sqrt{2}\)

(C) \(6\pi\)

(D) \(8\pi\)

(E) 16


Show Spoiler
Attachment:
2018-03-16_1011_003.png

23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 24 Apr 2024
Posts: 2,856
Own Kudos:
5,581
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,856
Kudos: 5,581
In the figure above, if semicircles A and B each have area 4pi 16 Mar 2018, 00:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


In the figure above, if semicircles A and B each have area \(4\pi\), what is the area of semicircle C?


(A) \(4\pi\)

(B) \(4\pi \sqrt{2}\)

(C) \(6\pi\)

(D) \(8\pi\)

(E) 16


Show Spoiler
Attachment:
2018-03-16_1011_003.png

Since both semi-circles A and B have the same area \(4*\pi\)
they will have similar radii(r), which can be calculated as follows:

\(\frac{1}{2}*\pi*r^2 = 4*\pi\) -> \(r^2 = 8\) ->\(r = 2\sqrt{2}\)

The diameter of the two semicircle \(2r = 4\sqrt{2}\) are the equal sides of an isosceles right-angled triangle.

The sides of these type of triangle are in the ratio \(1:1:\sqrt{2}\).

The hypotenuse of this right-angled triangle is the diameter of the semicircle C, which is \(\sqrt{2} * 4\sqrt{2} = 8\)

Therefore, the area of the semicircle C is \(\frac{1}{2}*\pi*r^2 = \frac{1}{2}*\pi*4^2 = 8*\pi\)(Option D)
User avatar
GMATinsight
User avatar
GMAT Club Legend
Joined: 08 Jul 2010
Last visit: 11 Dec 2024
Posts: 6,069
Own Kudos:
14,592
 [1]
Given Kudos: 125
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,069
Kudos: 14,592
 [1]
In the figure above, if semicircles A and B each have area 4pi 16 Mar 2018, 01:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


In the figure above, if semicircles A and B each have area \(4\pi\), what is the area of semicircle C?


(A) \(4\pi\)

(B) \(4\pi \sqrt{2}\)

(C) \(6\pi\)

(D) \(8\pi\)

(E) 16


Show Spoiler
Attachment:
2018-03-16_1011_003.png

Area of semicircle A and B = 4π = (1/2)πr^2
'i.e.Radius of semicircles A and B = 2√2
i.e. Diameter of semicircles A and B = 4√2

i.e. Hypotenuse of right triangle = Diameter of Semicircle C = √2 *4√2 (Using 45º-45º-90º triangle ratio)

i.e. Diameter of Circle C = 8
i.e. RAdius of semicircle C = 4

Area of Semicircle = (1/2)π4^2 = 8π

Answer: option D
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Dec 2024
Posts: 19,855
Own Kudos:
24,264
Given Kudos: 288
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,855
Kudos: 24,264
In the figure above, if semicircles A and B each have area 4pi 19 Mar 2018, 16:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


In the figure above, if semicircles A and B each have area \(4\pi\), what is the area of semicircle C?


(A) \(4\pi\)

(B) \(4\pi \sqrt{2}\)

(C) \(6\pi\)

(D) \(8\pi\)

(E) 16

Show Spoiler
Attachment:
2018-03-16_1011_003.png

Since area = πr^2, we see that a semicircle area is (1/2)(πr^2). Thus, for either semicircle, we can solve for the radius:

(1/2)(πr^2) = 4π

r^2 = 8

r = 2√2

The radius of each semicircle is 2√2, so the diameter of each of the semicircles A and B is 4√2.

The diameter of semicircle A is the length of one of the legs of the triangle, and the diameter of semicircle B is the length of the other leg. We can thus use the Pythagorean theorem to determine the length of the hypotenuse of the triangle, which is also the diameter of semicircle C.

(4√2)^2 + (4√2)^2 = c^2

32 + 32 = c^2

64 = c^2

8 = c

So the radius of semicircle C is 4, and hence the area of semicircle C is:

(1/2)(π x 4^2) = (1/2)(16π) = 8π

Answer: D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,795
Own Kudos:
929
Posts: 35,795
Kudos: 929
In the figure above, if semicircles A and B each have area 4pi 07 Jul 2022, 05:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Bunuel
Math Expert
97842 posts