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

 It is currently 23 Jan 2020, 04:46

### 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

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

# If the circle above has center A and area 144π , what is the perimete

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60625
If the circle above has center A and area 144π , what is the perimete  [#permalink]

### Show Tags

06 Jun 2017, 11:41
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:40) correct 22% (02:14) wrong based on 54 sessions

### HideShow timer Statistics

If the circle above has center A and area 144π, what is the perimeter of sector ABCD?

A. 12+3/2*π

B. 12+3π

C. 18+3/2*π

D. 24+3/2*π

E. 24+3π

Attachment:

CircleA.png [ 10.17 KiB | Viewed 1218 times ]

_________________
Senior Manager
Joined: 24 Apr 2016
Posts: 313
Re: If the circle above has center A and area 144π , what is the perimete  [#permalink]

### Show Tags

06 Jun 2017, 13:18
Radius of the circle = 12
Circumference of the circle = 24π

perimeter of sector ABCD = (Radius * 2) + $$\frac{45}{360}$$ * 24π

= 24 + 3π

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15965
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the circle above has center A and area 144π , what is the perimete  [#permalink]

### Show Tags

02 Dec 2019, 12:04
Hi ALL,

We're told that the circle above has center A and its area is 144pi. We're asked for the perimeter of sector ABCD. This question is based on several Geometry formulas - and we're given all of the necessary numbers to work with - so we just have to work through the appropriate math to answer it.

To start, ABCD is composed of 2 radii and a section of the circumference. That arc is based on a 45-degree angle, so it is 45/360 = 1/8 of the total circumference.

With an area of 144pi, we can solve for the radius:

Area = (pi)(R^2) = 144pi
R^2 = 144
R = 12

With a radius of 12, the total circumference is (2)(pi)(R) = (2)(pi)(12) = 24pi. The arc of ABCD is (1/8)(24pi) = 3pi

Thus, the total perimeter of ABCD is 12+12+3pi = 24 + 3pi

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: If the circle above has center A and area 144π , what is the perimete   [#permalink] 02 Dec 2019, 12:04
Display posts from previous: Sort by