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ANSWER
60 parts
EXPLANATION
In the model, we have 10 parts, where 6 are shaded to represent 6/10. Now we want a model where the whole is divided into 100 parts, which is 10 times as before. To represent the same fraction, we have to multiply the shaded regions by 10 as well. Thus, the number of parts that would be shaded in the new model would be 60 parts, to represent 6/10.