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

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Intern
Joined: 21 Sep 2006
Posts: 42
A thin piece of wire 40 meters long is cut into two pieces.  [#permalink]

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Updated on: 12 Dec 2013, 01:55
9
19
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:11) correct 32% (01:20) wrong based on 399 sessions

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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. $$\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-thin-piece-of-paper-40-mt-long-106671.html

Originally posted by $uckafr33 on 14 Oct 2006, 23:10. Last edited by Bunuel on 12 Dec 2013, 01:55, edited 1 time in total. Renamed the topic, edited the question, added the OA and moved to PS forum. Senior Manager Joined: 30 Aug 2006 Posts: 360 ### Show Tags 15 Oct 2006, 01:55 1 E ((40 - 2pi r)/4*(40 - 2pi r)/4) + pir^2 (1600 - 80pir -80pir + 4pi^2r^2)/16 + pir^2 100 - 10pir + (4pi^2^r^2 / 16) + pir^2 100 - 10pir + pi^2r^2/4 + pir^2 pir^2 + (10 - 1/2pir)^2 Manager Joined: 14 Jan 2006 Posts: 86 Schools: HKUST Re: Gmat Powerprep Word Problem [#permalink] ### Show Tags 15 Oct 2006, 02:04 1$uckafr33 wrote:
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?

a) pi r^2

b) pi r^2 +10

c) pi r^2 + 1/4 pi^2 r^2

d) pi r^2 + (40 - 2 pi r)^2

e) pi r^2 + (10 - 1/2 pi r)^2

Let the first peice be x meters in length, other side = 40-x
circumference of circle = x; 2pi r = x;
area of circle + area of square
pi r^2 + ((40-x)/4)^2;
pi r^2 + (10-2pi r/4)^2
pi r^2 + (10-pi r/2)^2;

E
Intern
Joined: 21 Sep 2006
Posts: 42

### Show Tags

15 Oct 2006, 05:57
OA is E. Thanks guys!
Retired Moderator
Joined: 05 Jul 2006
Posts: 1722

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15 Oct 2006, 08:16
1
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?

a) pi r^2 b) pi r^2 +10 c) pi r^2 + 1/4 pi^2 r^2 d) pi r^2 + (40 - 2 pi r)^2
e) pi r^2 + (10 - 1/2 pi r)^2

TWO PIECES = X,40-X

CIRCOM OF CIRCLE = 2Pi r = x thus circom of square = 40-2Pir and thus area = (10-1/2pir)^2

Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: A thin piece of wire 40 meters long is cut into two pieces.  [#permalink]

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12 Dec 2013, 01:55
17
12
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: a-thin-piece-of-paper-40-mt-long-106671.html
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Posts: 9427
Re: A thin piece of wire 40 meters long is cut into two pieces.  [#permalink]

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25 Jul 2018, 20:02
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).

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Re: A thin piece of wire 40 meters long is cut into two pieces. &nbs [#permalink] 25 Jul 2018, 20:02
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