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Annulus

Problem

A circle has a unit circle (radius, r = 1) removed from its centre to produce an annulus.


If the area remaining is the same as the unit circle removed, find the width of the annulus.


Solution

Let the radius of the original circle be, r.


If the area remaining is equal to the area removed (a unit circle), the area of the original circle will be twice a unit circle.

therefore πr2 = 2π implies r2 = 2.

Hence, the radius of the original circle, r = radical2 and so the width of the annulus is radical2 minus 1.

Problem ID: 159 (Mar 2004)     Difficulty: 2 Star

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