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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