The figure above shows the top side of a circular medallioin made of a circular piece of 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 medal frame is s centimeters, then in terms of s and r, what is the area of the metal frame, in square centimeters?
1. pi (r-s)^2
2. pi(r^2 - s^2)
3. 2pi( r-s)
4. r pie(2r - s)
5. pie s ( 2r - s)
Let r=3 and s=2.
Area of the whole medallion = �r² = �(3²) = 9�.
Radius of the circular glass center = r-s = 3-2 = 1.
Area of the circular glass center = �(1²) = �.
Area of the frame = medallion area - center area = 9� - � = 8�. This is our target.
Now we plug r=3 and s=2 into the answers to see which yields our target of 8�.
A quick scan of the answers reveals that only
E works:
�s(2r - s) = �(2)(2*3 - 2) = 8�.
The correct answer is
E.
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