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Area of region traced by spheres

A sphere of radius 1 is covered in ink and rolled around between concentric spheres of radii 3 and 5. If this process traces a region of area 1 on the larger sphere, what is the area of the region traced on the smaller sphere?

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The figure drawn on the smaller sphere is just a scaled down ...

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Area of region traced by smaller sphere rolling on another sphere

$2.19