geometry confusion

[awilhelm]

Picture the top side of a circular medallion made of a circular piece of glass surrounded by a metal frame. If the radius of the medallion is r centimeters and the width of the metal frame is s centimeters, then in terms of s and r, what is the area of the metal frame, in square centimeters?

a) pi(r-s)^2
b) pi(r^2 - s^2)
c) 2pi(r-s)
d) pi*r(2r - s)
e) pi*s(2r - s)

I approached this problem two different ways and end up with the wrong answer both times. Could someone tell me where I'm going wrong?

Approach 1 --> Plug in values
Let r = 4
Let s = 1

Area of metal frame = Total Area - Area of glass medallion

Total area = Pi * (4 + 1)^2 = 25pi
Area of glass medallion = Pi * 4^2 = 16pi
Area of metal frame = 25pi - 16pi = 9pi

Plug my values into answer choice a and we get --> pi(4-1)^2 = 9pi, so this should be correct, but it isn't!

Approach 2 --> Algebra

Area of metal frame = Total Area - Area of glass medallion
Total area = Pi*(r + s)^2
Area of glass medallion = (Pi)(r^2)
Area of metal frame = (Pi)(r + s)^2 - (Pi)(r^2)

Pi(r^2 + 2rs + s^2) - Pi(r^2)

Pi(r^2) + 2Pi(rs) + Pi(s^2) - Pi(r^2)

2Pi(rs) + Pi(s^2)

Pi(s)(2r + s)

But this also isn't correct. What am I doing wrong?

[awilhelm]

Please disregard, issue solved! Thanks.

[DanaJ]

The way I see this you have two circles with the same center. The bigger circle is the outer rim of the medallion and has a radius of r + s, with a surface of Pi*r ^2. This area encloses both the metal frame and the circular piece of glass. Now you have a second circle, which is actually the piece of glass, with an area of Pi*(r - s)^2. So by my calculations the surface of the metal frame is:

Pi*r ^2 - Pi*(r - s)^2 = Pi*(r^2 - r^2 + 2sr - s^2) = Pi*s(2r - s). Is E OA?

[chintudave]

IMO your algebra is correct. That is if i interpret the question correctly. What is the answer and what was the miss ?

[maihuna]

I also miss this question, this bloody english saying that r is the outer and s included....i did calculations as r and s...lost cool as well...lost almost several minutes on this q...bloody medallition

[altercator32]

33. The graph of which of the following equations have two intersections with axis-x?
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(C) y=-3x^2-5x+7
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1


Can anyone help me with this one ...