The figure shows the top side of a circular medallion made of a circul

Question

https://gmatclub.com/forum/download/file.php?id=23477 The figure shows the top side of a circular medallion made of a circular piece of colored glass surrounded by a metal frame, represented by the shaded region. If the radius of the medallion is r centimeters and the width of the metal frame is s centimeters, what is the area of the metal frame in terms of r and s? A. \pi(r-s)^2 B. \pi(r^2-s^2) C. 2\pi(r-s) D. \pi{r}(2r-s) E. \pi{s}(2r-s) m1.jpg m1.jpg Untitled.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=23477 
 The figure shows the top side of a circular medallion made of a circular piece of colored glass surrounded by a metal frame, represented by the shaded region. If the radius of the medallion is  r  centimeters and the width of the metal frame is s centimeters, what is the area of the metal frame in terms of r and s?

A.  \pi(r-s)^2

B.  \pi(r^2-s^2)

C.  2\pi(r-s)

D.  \pi{r}(2r-s)

E.  \pi{s}(2r-s)

Radius of the big circle = r.
Width of the frame = s.

Radius of the little circle = r - s.

Area of the frame = \pi*r^2-\pi*(r-s)^2=\pi(r^2-r^2+2rs-s^2)=\pi*s*(2r-s)

Answer: E.

sriharimurthy · Answer

Radius of medallion = r

Radius of circular piece of glass (medallion minus the metal frame) = (r-s)

Area of medallion =  pi*r^2  = A

Area of circular piece of glass (medallion minus the metal frame) =  pi*(r-s)^2  = B

Area of metal frame = A - B =  pi*r^2 - pi*(r-s)^2

=  pi*{r^2 - (r^2 + s^2 - 2rs)}

= pi*s*(2r - s)

sriharimurthy · Answer

Haha. You beat me to it!

Btw.. how do you get the symbol for pi?

Bunuel · Answer

Mark \pi with formula button  .

sriharimurthy · Answer

\pi  <img src="{SMILIES_PATH}/icon_biggrin.gif" alt=":-D" title="Very Happy" />

Cheers!

sriharimurthy · Answer

Hi,

The mistake you are making is that  you are considering 'r' to be the radius of the medallion  without  the glass frame.

The question states that the medallion is made of :
1) Circular piece of glass and
2) Metal frame

Also, we are told that the  radius 'r' is that of the medallion.

Given the width of the metal frame to be s, we can conclude that the  radius of the just the circular piece of glass will be (r-s).

Thus the expression is in fact as follows :

Area of the frame = \pi*r^2-\pi*(r-s)^2=\pi(r^2-r^2+2rs-s^2)=\pi*s*(2r-s) 
 
 Answer : E

dimitri92 · Answer

radius = r (cm)
width = s (cm) 
Area of the metal frame = ? (cm^2)

Think of this as concentric circles. Then the inner circle will have radius = r - s

The outer circle radius = r

The area of metal frame = Pi(r )^2- Pi(r-s)^2 
 = Pi(r^2 - s^2 +2sr - r^2) = Pi*s(2r - s )

my answer: E

whiplash2411 · Answer

You're given that the width of the medallion is s cm. And that the radius of the medallion is r cm. So the figure looks like this:

Attachment:

Medallion.jpg [ 25.89 KiB | Viewed 27420 times ]

Area of the medallion =\(\pi*r^2\)

Area of the frame = Area of the frame + medallion - Area of the medallion \(= \pi*(r+s)^2 - \pi*r^2 = \pi * [(r+s)^2 - (r)^2] = \pi * ( r+s+r) (r+s-r) = \pi*(s)(2r+s)\)

I'm not sure why the OA has a - sign either.

LJ · Answer

The question is worded somewhat awkwardly, which I believe is causing you to not picture the medallion correctly. We are asked to find the area of the metal frame, the area of which is  part  of radius  r .

Given:

Area of the whole medallion ( frame  +  glass center ):  \pi r^2 
The width of the frame is  s , so the area of just the glass center is:  \pi r^2 - \pi (r-s)^2

Solve:

\pi r^2 - \pi (r^2 - 2rs + s^2)

\pi r^2 - \pi r^2 - \pi s^2 + 2\pi rs

2\pi rs - \pi s^2

Pull out  \pi s  and you're left with   \pi s(2r - s)

shrouded1 · Answer

Area = Area(Bigger Circle) - Area(Smaller Circle)
 =  \pi (r)^2 - \pi (r-s)^2 
 =  \pi (-s^ + 2rs) 
 =  \pi s (2r-s)

Note that r is the radius of the medallion, or the bigger circle.

Hence, answer (e)

rishabhsingla · Answer

Darn! I thought the smaller circle has r and the bigger had r+s...

Thanks, shrouded1

NoHalfMeasures · Answer

i was wondering if it was somehow possible to hide answer from the screenshot? thanks!

Bunuel · Answer

Done. Similar questions to practice about rectangles: a-square-wooden-plaque-has-a-square-brass-inlay-in-the-89215.html a-border-of-uniform-width-is-placed-around-a-rectangular-144434.html a-rectangular-yard-is-20-yards-wide-and-40-yards-long-it-is-8453.html the-figure-above-represents-a-square-plot-measuring-x-feet-o-160568.html Similar questions to practice about circles: marty-s-pizza-shop-guarantees-that-their-pizzas-all-have-a-148428.html a-circular-lawn-with-a-radius-of-5-meters-is-surrounded-by-a-154737.html the-figure-above-shows-a-circular-flower-bed-with-its-cente-144448.html Hope it helps.

megha_2709 · Answer

Does anyone else think question is really ambiguous ? .By Radius of circular medallion I thought it meant radius of small circle. Hence I calculated it this way.
Radius of medallion i.e. small circle = r, radius of metal frame = s
Total radius of medallion + metal frame = r+s
Total area of medallion + metal frame = pi * (r+s)^2
Area of metal frame = (Total area of medallion + metal frame) - area of small circle
pi*(r+s)^2 - pi*r^2. = pi*s(s+2r)

after doing all this calculation I noticed my ans is not matching with any of the answer choices , so I did the calculation again with the correct understanding.

. I understand such silly mistake of mine will have worse consequences in actual GMAT Exam. My question is how to avoid such mistakes. Please please please help.

Regards
Megha

. I understand such silly mistake of mine will have worse consequences in actual GMAT Exam. My question is how to avoid such mistakes. Please please please help. Regards Megha

dave13 · Answer

Hey pushpitkc the solution istelf i understand, i just got stuck in agebraic technical details

we know thise formula, (a-b)^2 = a^2-2ab+b^2 so, pi*r^2- pi(r-s)^2 = pi*r^2- pi (r^2 -2rs+s^2) now what

pushpitkc · Answer

Hey  dave13

\pi*r^2 - \pi(r-s)^2 = \pi*r^2 - \pi (r^2 - 2rs + s^2) = \pi*r^2 - \pi*r^2 + \pi*2rs - \pi*s^2

Now we are left with  \pi*2rs - \pi*s^2 = s*\pi(2r - s) (when we take s common from both the terms)

Hope this helps you!

Jsound996 · Answer

Here's an alternative response, just plug in numbers!
Lets say that r=5 and s=2.
That means the area of the whole medallion is 25π, and the area of the medallion without the metal frame is 9π (r-s = 5-2 = 3 to find the radius of the inner circle)
That means the area of the metal frame is 16π
To find the area of the metal ring, substitute the values of r and s in the answer choices.
Only Answer E gives you 16π!

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The figure shows the top side of a circular medallion made of a circul

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