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A thermos bottle in the shape of a cylinder has an inner radius of 4.0 cm,...

A thermos bottle in the shape of a cylinder has an inner radius of 4.0 cm, an outer radius of 4.5 cm, and a lengt of 30cm. The insulating walls have a thermal conductivity equal to 2.0 x 10^-5 cal/(sec-cm celsius). One liter of hot coffee at 90 degrees Celsius is poured into the bottle. If the outside wall remains at 20 degrees Celsius, how long does it take for the coffee to cool to 50 degrees Celsius?

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