Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 08:36

### 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

# A thin piece of wire 40 meters long is cut into two pieces. One piece

Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Jun 2009
Posts: 31
Location: Stockholm, Sweden
Followers: 0

Kudos [?]: 3 [0], given: 0

A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

### Show Tags

15 Jun 2009, 00:35
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:30) correct 38% (01:30) wrong based on 78 sessions

### HideShow timer Statistics

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius R, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and square regions in terms of R.

1) $$\pi R^2$$
2) $$\pi R^2 + 10$$
3) $$\pi R^2 + 1/4\pi^2R^2$$
4) $$\pi R^2 + (40 - 2\pi R)^2$$
5) $$\pi R^2 + (10 - 1/2\pi R)^2$$

[Reveal] Spoiler:
4) or 5) is a given, I just dont see how you make the calculation necessary.
[Reveal] Spoiler: OA
Current Student
Joined: 03 Aug 2006
Posts: 115
Followers: 4

Kudos [?]: 265 [2] , given: 3

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

### Show Tags

15 Jun 2009, 01:15
2
KUDOS

Given:
40 meters long wire cut into two pieces.

Now Length of piece one = circumference of a circle with radius R = $$2\pi R$$

Length of piece two = perimeter of a square created using the remaining wire = $$40-2\pi R$$

$$\Rightarrow \text{length of each side of square} = \frac{40-2\pi R}{4}$$

$$= \frac{4(10-\frac{1}{2}\pi R)}{4}$$

$$= 10-\frac{1}{2}\pi R$$

Now
$$\text{Area of circle} = \pi R^2$$
$$\text {Area of square} = (10-\frac{1}{2}\pi R)^2$$

$$\text {Sum of the areas}=\pi R^2 + (10-\frac{1}{2}\pi R)^2$$
Manager
Joined: 07 Jun 2009
Posts: 209
Followers: 1

Kudos [?]: 40 [0], given: 9

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

### Show Tags

15 Jun 2009, 03:01
Option 'E' is correct.
_________________

Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 266
Location: Kuwait
Schools: Columbia university
Followers: 5

Kudos [?]: 306 [0], given: 52

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

### Show Tags

07 Jan 2012, 11:49
GREAT EXPLANATION NOOKWAY. THANK YOU
_________________

Sky is the limit

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15399
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

### Show Tags

10 May 2016, 12:10
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.
_________________
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece   [#permalink] 10 May 2016, 12:10
Similar topics Replies Last post
Similar
Topics:
1 A thin piece of cable 90 meters long is cut into two pieces. 2 13 Nov 2014, 07:04
1 A rope 40 feet long is cut into two pieces. If one piece is 14 25 May 2016, 08:48
129 A thin piece of wire 40 meters long is cut into two pieces. 33 11 May 2017, 06:50
22 A 5 meter long wire is cut into two pieces. If the longer 23 19 May 2017, 01:15
5 A 5 meter long wire is cut into two pieces. If the longer pi 5 21 Jun 2014, 06:28
Display posts from previous: Sort by