Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 154

A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
21 Dec 2010, 07:20
10
This post received KUDOS
63
This post was BOOKMARKED
Question Stats:
67% (01:04) correct 33% (01:16) wrong based on 1328 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 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. \(\pi*r^2 + (10  \frac{1}{2}\pi*r)^2\)
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: A THIN PIECE OF PAPER 40 MT LONG [#permalink]
Show Tags
21 Dec 2010, 07:38
44
This post received KUDOS
Expert's post
53
This post was BOOKMARKED
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 \(402\pi{r}\) meters of wire left for a square. Side of this square will be \(\frac{402\pi{r}}{4}=10\frac{\pi{r}}{2}\), hence the area of the square will be \((10\frac{\pi{r}}{2})^2\). The total area will be  \(\pi{r^2}+(10\frac{\pi{r}}{2})^2\). Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 28 Aug 2010
Posts: 257

Re: A THIN PIECE OF PAPER 40 MT LONG [#permalink]
Show Tags
23 Jan 2011, 15:04
Bunuel...how did u get side of the square as (402pi*r)/4 ?
_________________
Verbal:newtotheverbalforumpleasereadthisfirst77546.html Math: newtothemathforumpleasereadthisfirst77764.html Gmat: everythingyouneedtoprepareforthegmatrevised77983.html  Ajit



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: A THIN PIECE OF PAPER 40 MT LONG [#permalink]
Show Tags
23 Jan 2011, 15:08



Intern
Joined: 14 Sep 2010
Posts: 20

1
This post received KUDOS
1
This post was BOOKMARKED
A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?
From a 40m rope, two equal parts of 20 represent, respectively, the circumference of Circle C and the perimeter of Square D.
1. Express the perimeter of D in terms of the circumference of C.
Perimeter + Circumference = 40
Perimeter = 40  C
2. Substitute accepted identities for perimeter and circumference.
4s = 40  2(pi)(r)
3. Express the side of the square in terms of r.
s = 10  (pi)(r)/2
4. Write area of circle and square in terms of r.
Area(C) + Area(D) = (pi)(r)^2 + s^2 = (pi)(r)^2 + (10  (pi)(r)/2)^2
5. Verify
2(pi)(r) = 20
r = 10/pi = 3.18 (approx. to hundredth)
s = (10  (pi)(r)/2) = 10 [3.14(3.18)]/2 = 5
The actual value of the side of the square derived from stating area of square in terms of r is consistent with its known perimeter.
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: 40 meters wire problem [#permalink]
Show Tags
16 Jan 2012, 01:52
PhilosophusRex 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.
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) \(\pi R^2 + (10  1/2\pi R)^2\)
4) or 5) is a given, I just dont see how you make the calculation necessary. Very minimal calculations are required if you assume a convenient value for R e.g. R = 7/2 since \(\pi = 22/7\) Circumference in this case \(= 2\pi*R = 2*(22/7)*(7/2) = 22\) So length of leftover wire = 18 Side of square = 18/4 Area of square = \((9/2)^2\) Now put R = 7/2 in the second half of the options you want to check. i.e. say you want to check option (E) \((10  1/2\pi R)^2 = [10  (1/2)*(22/7)*(7/2)]^2 = (9/2)^2\) Option (E) is correct since the area of the square is (9/2)^2 when R = 7/2 (as shown above)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 136

Tried to solve this using the numbers given but I am not able to proceed. Please help. Just curious to know. Thanks. Say the length of each piece = 20. So Circumference =20 perimeter of square = 4*side So length of side = 20/4 = 5. How do I proceed further?
_________________
My First Blog on my GMAT Journey
Arise, Awake and Stop not till the goal is reached



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: wire [#permalink]
Show Tags
05 Mar 2012, 07:53
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
ENAFEX wrote: Tried to solve this using the numbers given but I am not able to proceed. Please help. Just curious to know. Thanks.
Say the length of each piece = 20.
So Circumference =20 perimeter of square = 4*side So length of side = 20/4 = 5.
How do I proceed further? The length of each piece = 20; Circumference of the circle is \(2\pi{r}=20\) > \(r=\frac{10}{\pi}\) > \(area=\pi{r^2}=\frac{100}{\pi}\); Perimeter of the square \(4*side=20\) > \(side=5\) > \(area=5^2=25\); The total area is \(\frac{100}{\pi}+25\). Now, you should substitute the value of \(r=\frac{10}{\pi}\) in the answer choices and see which one gives \(\frac{100}{\pi}+25\). Answer choice E works. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 07 May 2013
Posts: 104

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
01 Dec 2013, 20:52
Let the perimeter of circle be x>2pi*r=x(1) Let the perimeter of square be 40x>4S=40x Substitute value of x from(1) >S=(40/4)(2pi*r/4) >S=10pi*r/2 >\(S^2=(10pi*r/2)^2\) Therefore total area is \(pi*r^2+(10pi*r/2)^2\)



Intern
Joined: 13 Aug 2012
Posts: 3

Re: A THIN PIECE OF PAPER 40 MT LONG [#permalink]
Show Tags
24 Dec 2013, 23:35
Bunuel 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 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 \(402\pi{r}\) meters of wire left for a square. Side of this square will be \(\frac{402\pi{r}}{4}=10\frac{\pi{r}}{2}\), hence the area of the square will be \((10\frac{\pi{r}}{2})^2\).
The total area will be  \(\pi{r^2}+(10\frac{\pi{r}}{2})^2\).
Answer: E. Bunuel the perimeter of the circle and the square are the same, so: 2(pi)r=4a (a being one side of the square). a= (pi)r/2 area of square in terms of r: a^2= (pi)^2*r^2/4 wont this mean that option c is also correct? what am I missing?



Verbal Forum Moderator
Joined: 15 Jun 2012
Posts: 1124
Location: United States

Re: A THIN PIECE OF PAPER 40 MT LONG [#permalink]
Show Tags
25 Dec 2013, 01:52
1
This post received KUDOS
gmarchanda wrote: Bunuel 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 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 \(402\pi{r}\) meters of wire left for a square. Side of this square will be \(\frac{402\pi{r}}{4}=10\frac{\pi{r}}{2}\), hence the area of the square will be \((10\frac{\pi{r}}{2})^2\).
The total area will be  \(\pi{r^2}+(10\frac{\pi{r}}{2})^2\).
Answer: E. Bunuel the perimeter of the circle and the square are the same, so: 2(pi)r=4a (a being one side of the square). a= (pi)r/2 area of square in terms of r: a^2= (pi)^2*r^2/4 wont this mean that option c is also correct? what am I missing? Hello. The question only says: A thin piece of wire 40 meters long is cut into two pieces, NOT into same length pieces. Thus, your assumption 2(pi)r=4a is wrong. Hope it's clear.
_________________
Please +1 KUDO if my post helps. Thank you.
"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."
Chris Bangle  Former BMW Chief of Design.



Intern
Joined: 04 Nov 2013
Posts: 19
Location: United States
GPA: 3.96
WE: Information Technology (Computer Software)

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
01 Jun 2014, 22:44
1
This post received KUDOS
A little confusion here: As the total length is 2πr + 4x = 40 => πr + 2x = 20
I assumed length 10 as the circumference of the circle and 10 as the perimeter of the square.
=> πr=10 and x=5 and computed the total area, which is πr²+x² => 100/π + 25 (1)
I then substituted this values in the answer choice to find out the matches with (1), choices C and E seem to match. Can someone please tell me what am I doing wrong.
Thanks, a



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
02 Jun 2014, 00:17



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
10 Nov 2014, 20:41
3
This post received KUDOS
In this problem, its not at all mentioned that "wire 40 meters long is cut into two equal pieces" We have to take a variable for distribution of 40 meters in square & circle. Refer diagram below: Attachment:
sqa.png [ 3.51 KiB  Viewed 14654 times ]
Let the perimeter of the square = d then circumference of the circle = 40d \(2\pi r = 40d\) \(d = 40  2\pi r\) ..................... (1) Area of Circle \(= \pi r^2\) .............. (2) Each side of square \(= \frac{d}{4} = \frac{40  2\pi r}{4} = 10  \frac{\pi r}{2}\) .................... From (1) Area of square \(= (10  \frac{\pi r}{2})^2\) Total Area \(= \pi r^2 + (10  \frac{\pi r}{2})^2\) Answer = E
_________________
Kindly press "+1 Kudos" to appreciate



SVP
Joined: 11 Sep 2015
Posts: 2058
Location: Canada

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
15 Nov 2015, 21:00
Quote: A thin piece of 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 term of r?
A) πr² B) πr² + 10 C) πr² + 1/4(π² * r²) D) πr² + (40  2π * r)² E) πr² + (10  1/2π * r)² Another approach is to plug in a value for r and see what the output should be. Let's say r = 0. That is, the radius of the circle = 0 This means, we use the ENTIRE 40meter length of wire to create the square. So, the 4 sides of this square will have length 10, which means the area = 100So, when r = 0, the total area = 100 We'll now plug r = 0 into the 5 answer choices and see which one yields an output of 100A) π( 0²) = 0 NOPE B) π( 0²) + 10 = 10 NOPE C) π( 0²) + 1/4(π² * 0²) = 0 NOPE D) π( 0²) + (40  2π 0)² = 1600 NOPE E) π( 0²) + (10  1/2π( 0))² = 100 PERFECT! Answer: E Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Senior Manager
Joined: 20 Aug 2015
Posts: 394
Location: India

A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
16 Nov 2015, 00:27
anilnandyala 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 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. \(\pi*r^2 + (10  \frac{1}{2}\pi*r)^2\) Given: 40 meters long wire is cut into two pieces. One circle with radius r and the rest is used to form a square Required: Total area of the circle and the square Since we are given the length of the wire, we should find the perimeters. Perimeter of the circle = \(2*\pi*r\) Hence left over wire after removing the circle = \(40  (2*\pi*r)\) We need to form a square from this length. In other words, this is the perimeter of the square and each side of a square is equal. Hence side of square = \(\frac{1}{4}(40  (2*\pi*r))\) = \(10  \frac{1}{2}\pi*r\) Area of the square = \((10  \frac{1}{2}\pi*r)^2\) Total required area = \(\pi*r^2 + (10  \frac{1}{2}\pi*r)^2\) Option E



Manager
Joined: 05 Jul 2015
Posts: 107
Concentration: Real Estate, International Business
GPA: 3.3

A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
25 Nov 2015, 20:08
It doesn't say HOW LONG the wire is cut sooooooo R=0 Perimeter of the Square = 40 Area of the square = 10^2 BAM!!!! Answer E. Still took me 2 minutes just to understand the question though. Oh wow, gmatprep had the same idea as me.



Senior Manager
Joined: 20 Aug 2015
Posts: 394
Location: India

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
26 Nov 2015, 01:02
DJ1986 wrote: It doesn't say HOW LONG the wire is cut sooooooo R=0 Perimeter of the Square = 40 Area of the square = 10^2 BAM!!!! Answer E. Still took me 2 minutes just to understand the question though. Oh wow, gmatprep had the same idea as me. Hi DJ1986, Quiet an interesting way to tackle the question But if we go by what you say, there is no circle at all. Whereas the question says "One piece is used to form a circle with radius r, and the other is used to form a square"



Manager
Joined: 05 Jul 2015
Posts: 107
Concentration: Real Estate, International Business
GPA: 3.3

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
27 Nov 2015, 12:07
TeamGMATIFY wrote: DJ1986 wrote: It doesn't say HOW LONG the wire is cut sooooooo R=0 Perimeter of the Square = 40 Area of the square = 10^2 BAM!!!! Answer E. Still took me 2 minutes just to understand the question though. Oh wow, gmatprep had the same idea as me. Hi DJ1986, Quiet an interesting way to tackle the question But if we go by what you say, there is no circle at all. Whereas the question says "One piece is used to form a circle with radius r, and the other is used to form a square" I thought about that and decided that maybe the circle is microscopically so small it may as well be rounded to zero or maybe the person just imagined cutting a wire and making a circle but never actually did. Either way 0+whatever=whatever



Manager
Joined: 03 Jan 2017
Posts: 193

Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
Show Tags
28 Mar 2017, 13:00
let's take a brief look, the whole wire was used, so we need to take into account perimetr of the both figures when calculating the area r is given, radius
Pr^2+((402Pr)/4)^2 We need to divide the latter by 4 because perimeter of a squae has 4 sides
Answer is E




Re: A thin piece of wire 40 meters long is cut into two pieces.
[#permalink]
28 Mar 2017, 13:00



Go to page
1 2
Next
[ 29 posts ]



