It is currently 20 Nov 2017, 12:44

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Quick facts for circle inscribed in a square and vice versa.

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 17 Mar 2011
Posts: 448

Kudos [?]: 187 [3], given: 5

Location: United States (DC)
Concentration: General Management, Technology
GMAT 1: 760 Q49 V45
GPA: 3.37
WE: Information Technology (Consulting)
Quick facts for circle inscribed in a square and vice versa. [#permalink]

### Show Tags

20 Apr 2011, 09:47
3
KUDOS
2
This post was
BOOKMARKED
I often spend way too much time re-solving for these, each time I encounter them.

Circle Inscribed In A Square
The circle will have radius r, and consequentially the square will have side 2r.
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 4r^2, or (pi)/4
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 8r, or (pi)/4
Conveniently, the ratios are both the same! :D

The difference in area is (4-pi)*r^2
The difference in perimeter is (8-2pi)*r

Square Inscribed in a circle
This one is harder to solve for, since you have to do some calculations to solve for either the radius or the side of a square.
Assuming the circle has radius r, and the square will have side r*sqrt(2).
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 2r^2, or (pi)/2
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 4r*sqrt(2), or (pi)/(2*sqrt(2))

The difference in area is (pi-2)*r^2
The difference in perimeter is (2pi - 4*sqrt(2))*r

Kudos [?]: 187 [3], given: 5

Non-Human User
Joined: 09 Sep 2013
Posts: 15617

Kudos [?]: 283 [0], given: 0

Re: Quick facts for circle inscribed in a square and vice versa. [#permalink]

### Show Tags

04 Jan 2015, 12:59
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.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15617

Kudos [?]: 283 [0], given: 0

Re: Quick facts for circle inscribed in a square and vice versa. [#permalink]

### Show Tags

20 Jun 2017, 10:23
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.
_________________

Kudos [?]: 283 [0], given: 0

Re: Quick facts for circle inscribed in a square and vice versa.   [#permalink] 20 Jun 2017, 10:23
Display posts from previous: Sort by