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GMAT Prep : Geometry

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by ashokkadam » Sat Oct 02, 2010 11:18 pm
area of metal frame = TT * (r+s)^2 - TT * r^2
= TT (2rs + s^2)
= TTs(2r -s)

hence E is the answer.
Skywalker wrote:Please find the sum uploaded as an image...I am not able to get the answer which is option 5.



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by narik11 » Sat Oct 02, 2010 11:59 pm
ashokkadam wrote:area of metal frame = TT * (r+s)^2 - TT * r^2
= TT (2rs + s^2)
= TTs(2r -s)

hence E is the answer.
Skywalker wrote:Please find the sum uploaded as an image...I am not able to get the answer which is option 5.



Image

It has to be TTs(2r+s) from ur calculation
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by ashokkadam » Sun Oct 03, 2010 12:54 am
Right! there was a typo. But the final answer is correct and that is what I meant.
anyways i have corrected below
narik11 wrote:
ashokkadam wrote:area of metal frame = TT * (r+s)^2 - TT * r^2
= TT (2rs - s^2)
= TTs(2r -s)

hence E is the answer.
Skywalker wrote:Please find the sum uploaded as an image...I am not able to get the answer which is option 5.



Image

It has to be TTs(2r+s) from ur calculation
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by GMATGuruNY » Sun Oct 03, 2010 3:27 am
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 and the width of the metal frame is s, what is the area of the metal frame in terms of r and s?

1. pi (r-s)^2
2. pi (r^2 -s^2)
3. 2pi(r-s)
4. pi*r*(2r-s)
5. pi*s*(2r-s)

Since there are variables in the answer choices, we can plug in values.

Let r = 3.
Then area of medallion = 9pi.
Let s = 1.
Then radius of glass = r-s = 3-1 = 2.
Area of glass = 4pi.
Area of frame = 9pi - 4pi = 5pi. This is our target answer.

Only answer choice E works:
pi*s*(2r-s) = pi*1*(2*3 - 1) = 5pi.

The correct answer is E.
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