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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

16 Sep 2012, 03:26

1

This post was BOOKMARKED

Pansi wrote:

If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12) B. a^2((pi-2)/4) C.a^2((9pi-16)/12) D.a((3pi-1)/12) E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square. Hence diagonal of a square with side x= x root2 => x root2 = a (radius of circle) =>x= a/root 2 Hence area of square = (a/root 2)^2 = a^2/2. Now the area of circular quadrant is (pi * a^2)/4 So shaded area = (pi * a^2)/4 - a^2/2, by simplifying => a^2((pi-2)/4) Hence Answer B.
_________________

Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

16 Sep 2012, 06:26

1

This post received KUDOS

1

This post was BOOKMARKED

SOURH7WK wrote:

Pansi wrote:

If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12) B. a^2((pi-2)/4) C.a^2((9pi-16)/12) D.a((3pi-1)/12) E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square. Hence diagonal of a square with side x= x root2 => x root2 = a (radius of circle) =>x= a/root 2 Hence area of square = (a/root 2)^2 = a^2/2. Now the area of circular quadrant is (pi * a^2)/4 So shaded area = (pi * a^2)/4 - a^2/2, by simplifying => a^2((pi-2)/4) Hence Answer B.

Just a remark: For any quadrilateral with perpendicular diagonals (so obviously also for a square), the area is given by half the product of the diagonals. (You can easily deduce it by expressing the areas of the triangles formed by the diagonals.)

So, when you know the diagonal of a square, you don't have to compute the side in order to find the area. You just have to square the diagonal and half it. In the given question, the diagonal of the square is \(a\) (the radius of the circle), so the area of the square is \(a^2/2.\)
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

13 Nov 2013, 14:57

SOURH7WK wrote:

Pansi wrote:

If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12) B. a^2((pi-2)/4) C.a^2((9pi-16)/12) D.a((3pi-1)/12) E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square. Hence diagonal of a square with side x= x root2 => x root2 = a (radius of circle) =>x= a/root 2 Hence area of square = (a/root 2)^2 = a^2/2. Now the area of circular quadrant is (pi * a^2)/4 So shaded area = (pi * a^2)/4 - a^2/2, by simplifying => a^2((pi-2)/4) Hence Answer B.

???? my answer is a square (a square (pi -1)/4) or asquare pi - 4 a square.!!!

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

09 May 2015, 02:36

Devon wrote:

Area of one quarter of the circle: (pi*a^2)/4

Area of the square:

Diagonal is equal to radius a. Therefore s(sqrt2) = a --> s = a/(sqrt2) s^2 = (a^2)/2

Area of the shaded region is area of one quarter of the circle minus area of the square:

(pi*a^2)/4 - (a^2)/2 = [(pi*a^2) - 2(a^2)]/4

Factor out a^2:

a^2[(pi-2)/4]

Answer is B

You have reduced qone quadrant with area of Square, I am fine with it. But I have worked out complete Area of circle minus Area of Square which gives= a^2(Pi-1/2). What is wrong in this?

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

08 Jun 2016, 08:20

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.
_________________

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...