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Area Between Two Concentric Circles

I have a word problem that requires me to find the area of the ring and the area of the circle where the area between each concentric circle is r which is the same as the smallest circles radius. How can I find the radius and compare them to each other? Would I use the standard formula of a circle?

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Area Between Two Concentric Circles is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.