SOLUTION: Picture of 2 circles... One inside the other. Area between the circles is shaded. Question: find the radius (of the smaller circle) if the width of the shaded region is 2cm and i

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Question 790139: Picture of 2 circles... One inside the other. Area between the circles is shaded.
Question: find the radius (of the smaller circle) if the width of the shaded region is 2cm and its area is 176cm2
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let the radius of the inner circle be . Then the radius of the outer circle is

There are 2 ways to describe the area of the outer circle. One way is the standard formula for the area of a circle, namely

But since the radius of the outer circle is , the area would be .

But the area of the outer circle can also be defined as the area of the inner circle plus the area of the shaded region. The area of the inner circle is just and the area of the shaded region is . Since these two ways of describing the same area must be equal:



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