Deepthi Subbu wrote:
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)
We can plug in values for r and s.
Let r=3 and s=1.
Area of medallion = pi(3^2) = 9pi.
Radius of circular glass = radius of medallion - width of frame = 3-1 = 2.
Area of circular glass = pi(2^2) = 4pi.
Area of frame = medallion - glass = 9pi-4pi = 5pi. This is our target answer.
Now we plug r=3 and s=1 into all the answers to see which yields our target of 5pi.
Only answer choice E works:
Pi*s*(2r-s) = pi*1*(2*3 - 1) = 5pi.
The correct answer is
E.
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