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Vinyl record groove length calculation

1425ApprenticeCalculusGeometry

Olimpiadas Matemáticas Españolas

A vinyl record rotates at a speed of $33 \frac{1}{3}$ revolutions per minute and its playback lasts 24 min $30 \mathrm{~s}$. The recorded part has an outer diameter of $29 \mathrm{~cm}$ and an inner diameter of 11.5 $\mathrm{cm}$. Using this data, calculate the length of the recorded groove.
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