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A roll of adhesive tape is wound round a central cylindrical core of radius $3 \; \text{cm}$. The outer radius of a roll containing $20 \; \text{m}$ of tape is $4 \; \text{cm}$. What is the outer radius of a roll containing $80 \; \text{m}$ of tape?

This problem is taken from the UKMT Mathematical Challenges.

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