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8-59.

THE RUSSIAN DOLL

For generations, special wooden dolls have been handcrafted in Russia. This type of cylindrical doll opens at the midsection and nested inside is a smaller wooden doll (with the same shape) which itself opens to another doll. Some dolls are made up of $10$ or more parts! The smallest doll, often less than a centimeter tall, is solid wood.

Explain why, under ideal conditions, the sum of the volumes of the nested wooden shells of the different-sized Russian Dolls would calculate the full volume of the interior of the largest doll.

An 'ideal' situation would have infinitely many dolls with infinitely small thicknesses.