It is currently 18 Jan 2018, 02:17

### 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: 29

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

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

### Show Tags

14 Jun 2009, 23:35
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:23) correct 36% (01:32) wrong based on 127 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-thin-piece ... 06671.html
[Reveal] Spoiler: OA

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

Current Student
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 320 [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, 00:15
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
$$\text{Area of circle} = \pi R^2$$
$$\text {Area of square} = (10-\frac{1}{2}\pi R)^2$$

$$\text {Sum of the areas}=\pi R^2 + (10-\frac{1}{2}\pi R)^2$$

Kudos [?]: 320 [2], given: 3

Manager
Joined: 07 Jun 2009
Posts: 204

Kudos [?]: 46 [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, 02:01
Option 'E' is correct.
_________________

Kudos [?]: 46 [0], given: 9

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: 251

Kudos [?]: 392 [0], given: 52

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

### Show Tags

07 Jan 2012, 10:49
GREAT EXPLANATION NOOKWAY. THANK YOU
_________________

Sky is the limit

Kudos [?]: 392 [0], given: 52

Non-Human User
Joined: 09 Sep 2013
Posts: 14251

Kudos [?]: 291 [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, 11:10
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.
_________________

Kudos [?]: 291 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 43317

Kudos [?]: 139367 [0], given: 12787

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

### Show Tags

21 Dec 2017, 23:09
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 the square regions in terms of r?

A. $$\pi*r^2$$
B. $$\pi*r^2 + 10$$
C. $$\pi*r^2 + \frac{1}{4}*\pi^2*r^2$$
D. $$\pi*r^2 + (40 - 2\pi*r)^2$$
E. $$\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2$$

The area of a circle will be - $$\pi{r^2}$$ and $$2\pi{r}$$ meters of wire will be used;
There will be $$40-2\pi{r}$$ meters of wire left for a square. Side of this square will be $$\frac{40-2\pi{r}}{4}=10-\frac{\pi{r}}{2}$$, hence the area of the square will be $$(10-\frac{\pi{r}}{2})^2$$.

The total area will be - $$\pi{r^2}+(10-\frac{\pi{r}}{2})^2$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-thin-piece ... 06671.html
_________________

Kudos [?]: 139367 [0], given: 12787

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece   [#permalink] 21 Dec 2017, 23:09
Display posts from previous: Sort by