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To answer the question would require knowledge of several variables that are not specified in the question - to wit:

Is "1 km" the diameter, radius, or circumference of the sphere?

What is the initial temperature of the sphere?

Is the sphere in contact with other matter or is it in a vacuum?

Is the sphere under pressure?

Does evaporation have to be accounted for?

If it is in contact with some other solid, liquid, gas, plasma, etc - what are the physical properties of the material(s) it is in contact with?

Is it radiating to a black body?

Is there any source of energy radiating back to the sphere?

Is the sphere in motion or stationary?

Is the sphere subject to any external fields such as magnetic fields?

I'm sure we could identify even more unspecified variables that would impact the answer, but the point is that the question cannot be answered without more information.

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Q: How long does it take for a 1 km sphere of molten iron to solidify?
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